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</div><h2>HL Paper 3</h2><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The weight of tea in <em>Supermug</em> tea bags has a normal distribution with mean 4.2 g and standard deviation 0.15 g. The weight of tea in <em>Megamug</em> tea bags has a normal distribution with mean 5.6 g and standard deviation 0.17 g.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find the probability that a randomly chosen <em>Supermug</em> tea bag contains more than 3.9 g of tea.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find the probability that, of two randomly chosen <em>Megamug</em> tea bags, one contains more than 5.4 g of tea and one contains less than 5.4 g of tea.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find the probability that five randomly chosen <em>Supermug</em> tea bags contain a total of less than 20.5 g of tea.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find the probability that the total weight of tea in seven randomly chosen <em>Supermug</em> tea bags is more than the total weight in five randomly chosen <em>Megamug</em> tea bags.</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">let <em>S</em> be the weight of tea in a random <em>Supermug</em> tea bag</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(S \sim {\text{N(4.2, 0.1}}{{\text{5}}^2})\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{P}}(S > 3.9) = 0.977\) <strong><em>(M1)A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">let <em>M</em> be the weight of tea in a random <em>Megamug</em> tea bag</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(M \sim {\text{N(5.6, 0.1}}{{\text{7}}^2})\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{P}}(M > 5.4) = 0.880 \ldots \) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{P}}(M < 5.4) = 1 - 0.880 \ldots = 0.119 \ldots \) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">required probability \( = 2 \times 0.880 \ldots \times 0.119 \ldots = 0.211\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[4 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{P}}({S_1} + {S_2} + {S_3} + {S_4} + {S_5} < 20.5)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">let \({S_1} + {S_2} + {S_3} + {S_4} + {S_5} = A\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{E}}(A) = 5{\text{E}}(S)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">= 21 <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{Var}}(A) = 5{\text{Var}}(S)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">= 0.1125 <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(A \sim {\text{N(21, 0.1125}})\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{P}}(A < 20.5) = 0.0680\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[4 marks]</em></strong></span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{P}}({S_1} + {S_2} + {S_3} + {S_4} + {S_5} + {S_6} + {S_7} - ({M_1} + {M_2} + {M_3} + {M_4} + {M_5}) > 0)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">let \({S_1} + {S_2} + {S_3} + {S_4} + {S_5} + {S_6} + {S_7} - ({M_1} + {M_2} + {M_3} + {M_4} + {M_5}) = B\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{E}}(B) = 7{\text{E}}(S) - 5{\text{E}}(M)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">= 1.4 <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;">Note:</strong><span style="font-family: 'times new roman', times; font-size: medium;"> Above </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>A1</em></strong><span style="font-family: 'times new roman', times; font-size: medium;"> is independent of first </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>M1</em></strong><span style="font-family: 'times new roman', times; font-size: medium;">.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{Var}}(B) = 7{\text{Var}}(S) + 5{\text{Var}}(M)\) </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>(M1)</em></strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">= 0.302 <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{P}}(B > 0) = 0.995\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[5 marks]</em></strong></span></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">For most candidates this was a reasonable start to the paper with many candidates gaining close to full marks. The most common error was in (b) where, surprisingly, many candidates did not realise the need to multiply the product of the two probabilities by 2 to gain the final answer. Weaker candidates often found problems in understanding how to correctly find the variance in both (c) and (d).</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">For most candidates this was a reasonable start to the paper with many candidates gaining close to full marks. The most common error was in (b) where, surprisingly, many candidates did not realise the need to multiply the product of the two probabilities by 2 to gain the final answer. Weaker candidates often found problems in understanding how to correctly find the variance in both (c) and (d).</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">For most candidates this was a reasonable start to the paper with many candidates gaining close to full marks. The most common error was in (b) where, surprisingly, many candidates did not realise the need to multiply the product of the two probabilities by 2 to gain the final answer. Weaker candidates often found problems in understanding how to correctly find the variance in both (c) and (d).</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">For most candidates this was a reasonable start to the paper with many candidates gaining close to full marks. The most common error was in (b) where, surprisingly, many candidates did not realise the need to multiply the product of the two probabilities by 2 to gain the final answer. Weaker candidates often found problems in understanding how to correctly find the variance in both (c) and (d).</span></p>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>Two species of plant, \(A\) and \(B\), are identical in appearance though it is known that the mean length of leaves from a plant of species \(A\) is \(5.2\) cm, whereas the mean length of leaves from a plant of species \(B\) is \(4.6\) cm. Both lengths can be modelled by normal distributions with standard deviation \(1.2\) cm.</p>
<p>In order to test whether a particular plant is from species \(A\) or species \(B\), \(16\) leaves are collected at random from the plant. The length, \(x\), of each leaf is measured and the mean length evaluated. A one-tailed test of the sample mean, \(\bar X\), is then performed at the \(5\% \) level, with the hypotheses: \({H_0}:\mu = 5.2\) and \({H_1}:\mu < 5.2\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the critical region for this test.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">It is now known that in the area in which the plant was found \(90\% \) of all the plants are of species \(A\) and \(10\% \) are of species \(B\).</p>
<p class="p1">Find the probability that \(\bar X\) will fall within the critical region of the test.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">If, having done the test, the sample mean is found to lie within the critical region, find the probability that the leaves came from a plant of species \(A\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>\(\bar X \sim N\left( {5.2,{\text{ }}\frac{{{{1.2}^2}}}{{16}}} \right)\) (<strong><em>M1)</em></strong></p>
<p>critical value is \(5.2 - 1.64485 \ldots \times \frac{{1.2}}{4} = 4.70654 \ldots \) <strong><em>(A1)</em></strong></p>
<p>critical region is \(] - \infty ,{\text{ }}4.71]\) <strong><em>A1</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Allow follow through for the final <strong><em>A1 </em></strong>from their critical value.</p>
<p> </p>
<p><strong>Note: </strong>Follow through previous values in (b), (c) and (d).</p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(0.9 \times 0.05 + 0.1 \times (1 - 0.361 \ldots ) = 0.108875997 \ldots = 0.109\) <strong><em>M1A1</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>M1 </em></strong>for a weighted average of probabilities with weights \(0.1,0.9\).</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>attempt to use conditional probability formula <strong><em>M1</em></strong></p>
<p>\(\frac{{0.9 \times 0.05}}{{0.108875997 \ldots }}\) <strong><em>(A1)</em></strong></p>
<p>\( = 0.41334 \ldots = 0.413\) <strong><em>A1</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<p><strong><em>Total [10 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">Solutions to this question were generally disappointing.</p>
<p class="p1">In (a), the standard error of the mean was often taken to be \(\sigma (1.2)\) instead of \(\frac{\sigma }{{\sqrt n }}(0.3)\) and the solution sometimes ended with the critical value without the critical region being given.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">In (c), the question was often misunderstood with candidates finding the weighted mean of the two means, ie \(0.9 \times 5.2 + 0.1 \times 4.6 = 5.14\) instead of the weighted mean of two probabilities.</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Without having the solution to (c), part (d) was inaccessible to most of the candidates so that very few correct solutions were seen.</p>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">The random variable \(X \sim {\text{Po}}(m)\). Given that P(<em>X </em>= <em>k </em>−1) = P(<em>X </em>= <em>k </em>+1), where <em>k </em>is a positive integer,</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">show that \({m^2} = k(k + 1)\);</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">hence show that the mode of <em>X </em>is <em>k </em>.</span></p>
<div class="marks">[6]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{{m^{k - 1}}{e^{ - m}}}}{{(k - 1)!}} = \frac{{{m^{k + 1}}{e^{ - m}}}}{{(k + 1)!}}\) <strong> <em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow 1 = \frac{{{m^2}}}{{(k + 1)k}}\) <strong> <em>A1</em></strong></span><strong style="font-family: 'times new roman', times; font-size: medium;"> </strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: </strong>Award <strong><em>A1 </em></strong>for any correct intermediate step.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow {m^2} = (k + 1)k\) <strong> <em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><strong><em><span style="font-family: 'times new roman', times; font-size: medium;">[2 marks]</span><br></em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{{\text{P}}(X = k)}}{{{\text{P}}(X = k - 1)}} = \frac{{{e^{ - m}} \times \frac{{{m^k}}}{{k!}}}}{{{e^{ - m}} \times \frac{{{m^{k - 1}}}}{{(k - 1)!}}}}\) <strong> <em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{m}{k}\) <strong> <em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{{\sqrt {k(k + 1)} }}{k}\) <strong> <em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \sqrt {\frac{{k + 1}}{k}} > 1\) <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">so \({\text{P}}(X = k) > {\text{P}}(X = k - 1)\) <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">similarly \({\text{P}}(X = k) > {\text{P}}(X = k + 1)\) <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">hence <em>k </em>is the mode <strong><em>AG<br></em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><strong><em><span style="font-family: 'times new roman', times; font-size: medium;">[6 marks]</span><br></em></strong></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Most candidates were able to complete part (a). The remainder of the question involved some understanding of the shape of the distribution and some facility with algebraic manipulation.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Most candidates were able to complete part (a). The remainder of the question involved some understanding of the shape of the distribution and some facility with algebraic manipulation.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">A traffic radar records the speed, \(v\) kilometres per hour (\({\text{km}}\,{{\text{h}}^{-{\text{1}}}}\)), of cars on a section of a road.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">The following table shows a summary of the results for a random sample of 1000 cars whose speeds were recorded on a given day.</span></p>
<p style="font: normal normal normal 20.5px/normal 'Times New Roman'; text-align: center; margin: 0px;"><br><span style="font-family: 'times new roman', times; font-size: medium;"><img src="images/Schermafbeelding_2014-09-18_om_07.17.39.png" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Using the data in the table,</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">(i) show that an estimate of the mean speed of the sample is 113.21 \({\text{km}}\,{{\text{h}}^{-{\text{1}}}}\);</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) find an estimate of the variance of the speed of the cars on this section of the road.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Find the 95% confidence interval, \(I\), for the mean speed.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: 'times new roman', times; font-size: medium;">Let \(J\) be the 90% confidence interval for the mean speed.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Without calculating \(J\), explain why \(J \subset I\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) \(\bar v = \frac{1}{{1000}}(55 \times 5 + 65 \times 13 + \ldots + 145 \times 31)\) <strong><em>A1M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: <em>A1</em> </strong>for mid-points, <strong><em>M1 </em></strong>for use of the formula.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{{113\,210}}{{1000}} = 113.21\) <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) \({s^2} = \frac{{{{(55 - 113.21)}^2} \times 5 + {{(65 - 113.21)}^2} \times 13 + \ldots + {{(145 - 113.21)}^2} \times 31}}{{999}}\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{{362\,295.9}}{{999}} = 362.6585 \ldots = 363\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: </strong>Award <strong><em>A1 </em></strong>if answer rounds to 362 or 363.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: </strong>Condone division by 1000.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[4 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\bar v \pm \frac{{{t_{0.025}} \times s}}{{\sqrt n }}\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">hence the confidence interval \(I = [112.028,{\text{ }}114.392]\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Accept answers which round to 112 and 114.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Condone the use of \({z_{0.025}}\) for \({t_{0.025}}\) and \(\sigma \) for \(s\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: 'times new roman', times; font-size: medium;">less confidence implies narrower interval <strong><em>R2</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Accept equivalent statements or arguments having a meaningful diagram and/or relevant percentiles.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">hence the confidence interval \(I\) at the 95% level contains the confidence interval \(J\) at the 90% level <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">In (a)(i), the candidates were required to show that the estimate of the mean is 113.21 so that those who stated simply ‘Using my GDC, mean = 113.21’ were given no credit. Candidates were expected to indicate that the interval midpoints were used and to show the appropriate formula. In (a)(ii), division by either 999 or 1000 was accepted, partly because of the large sample size and partly because the question did not ask for an unbiased estimate of variance.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Solutions to (c) were often badly written, often quite difficult to understand exactly what was being stated.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The random variable <em>X</em> has the distribution \({\text{B}}(n{\text{ , }}p)\) .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) (i) Show that \(\frac{{{\text{P}}(X = x)}}{{{\text{P}}(X = x - 1)}} = \frac{{(n - x + 1)p}}{{x(1 - p)}}\) .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) Deduce that if \({\text{P}}(X = x) > {\text{P}}(X = x - 1)\) then \(x < (n + 1)p\) .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(iii) Hence, determine the value of <em>x</em> which maximizes \({\text{P}}(X = x)\) when \((n + 1)p\) is not an integer.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) Given that <em>n</em> = 19 , find the set of values of <em>p</em> for which <em>X</em> has a unique mode of 13.</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) (i) \(\frac{{{\text{P}}(X = x)}}{{{\text{P}}(X = x - 1)}} = \frac{{\left( {\frac{{n!}}{{(n - x)!x!}} \times {p^x} \times {{(1 - p)}^{n - x}}} \right)}}{{\left( {\frac{{n!}}{{(n - x + 1)!(x - 1)!}} \times {p^{x - 1}} \times {{(1 - p)}^{n - x + 1}}} \right)}}\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{{(n - x + 1)p}}{{x(1 - p)}}\) <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) if \({\text{P}}(X = x) > {\text{P}}(X = x - 1)\) then</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\((n - x + 1)p > x(1 - p)\) <strong><em>(M1)A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(np - xp + p > x - px\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(x < (n + 1)p\) <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(iii) to maximise the probability we also need</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{P}}(X = x) > {\text{P}}(X = x + 1)\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{\left( {n - (x + 1) + 1} \right)p}}{{(x + 1)(1 - p)}} < 1\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(np - xp < x - xp + 1 - p\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(p(n + 1) < x + 1\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">hence \(p(n + 1) > x > p(n + 1) - 1\) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">so <em>x</em> is the integer part of </span><span style="font-family: 'times new roman', times; font-size: medium;">\((n + 1)p\) </span><em style="font-family: 'times new roman', times; font-size: medium;">i.e.</em><span style="font-family: 'times new roman', times; font-size: medium;"> the largest integer less than \((n + 1)p\) </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>A1</em></strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[9 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) the mode is the value which maximises the probability <strong><em>(R1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(20p > 13 > 20p - 1\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow p > \frac{{13}}{{20}} = 0.65\), and \(p < \frac{7}{{10}} = 0.70\) <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(it follows that \(0.65 < p < 0.7\))</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[4 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>Total [13 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Many candidates made a reasonable attempt at (a)(i) and (ii) but few were able to show that the mode is the integer part of \((n + 1)p\). Part (b) also proved difficult for most candidates with few correct solutions seen.</span></p>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Each week the management of a football club recorded the number of injuries suffered by their playing staff in that week. The results for a 52-week period were as follows:</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Calculate the mean and variance of the number of injuries per week.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Explain why these values provide supporting evidence for using a Poisson distribution model.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">mean = 2.06 <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">variance = 1.94 <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">a Poisson distribution has the property that its mean and variance are the same <strong><em>R1<br></em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><strong><em><span style="font-family: 'times new roman', times; font-size: medium;">[1 mark]</span><br></em></strong></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Many candidates picked up good marks for this question, but lost marks because of inattention to detail. The mean of the data was usually given correctly, but sometimes the variance was wrong. It may seem a small point, but the correct hypotheses should not mention the value of the estimated mean. Some candidates did not notice that some columns needed to be combined.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Many candidates picked up good marks for this question, but lost marks because of inattention to detail. The mean of the data was usually given correctly, but sometimes the variance was wrong. It may seem a small point, but the correct hypotheses should not mention the value of the estimated mean. Some candidates did not notice that some columns needed to be combined.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>If \(X\) is a random variable that follows a Poisson distribution with mean \(\lambda > 0\) then the probability generating function of \(X\) is \(G(t) = {e^{\lambda (t - 1)}}\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> </span>Prove that \({\text{E}}(X) = \lambda \).</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>Prove that \({\text{Var}}(X) = \lambda \).</p>
<div class="marks">[6]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">\(Y\) is a random variable, independent of \(X\), that also follows a Poisson distribution with mean \(\lambda \).</p>
<p class="p1">If \(S = 2X - Y\) find</p>
<p class="p1">(i) <span class="Apple-converted-space"> </span>\({\text{E}}(S)\);</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>\({\text{Var}}(S)\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Let \(T = \frac{Y}{2} + \frac{Y}{2}\).</p>
<p class="p1">(i) <span class="Apple-converted-space"> </span>Show that \(T\) is an unbiased estimator for \(\lambda \).</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>Show that \(T\) is a more efficient unbiased estimator of \(\lambda \) than \(S\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Could either \(S\) or \(T\) model a Poisson distribution? Justify your answer.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">By consideration of the probability generating function, \({G_{X + Y}}(t)\), of \(X + Y\), prove that \(X + Y\) follows a Poisson distribution with mean \(2\lambda \).</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find</p>
<p class="p1">(i) <span class="Apple-converted-space"> </span>\({G_{X + Y}}(1)\);</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>\({G_{X + Y}}( - 1)\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Hence find the probability that \(X + Y\) is an even number.</p>
<div class="marks">[3]</div>
<div class="question_part_label">g.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>(i) \(G'(t) = \lambda {e^{\lambda (t - 1)}}\) <strong><em>A1</em></strong></p>
<p>\({\text{E}}(X) = G'(1)\) <strong><em>M1</em></strong></p>
<p>\( = \lambda \) <strong><em>AG</em></strong></p>
<p>(ii) \(G''(t) = {\lambda ^2}{e^{\lambda (t - 1)}}\) <strong><em>M1</em></strong></p>
<p>\( \Rightarrow G''(1) = {\lambda ^2}\) <strong><em>(A1)</em></strong></p>
<p>\({\text{Var}}(X) = G''(1) + G'(1) - {\left( {G'(1)} \right)^2}\) <strong><em>(M1)</em></strong></p>
<p>\( = {\lambda ^2} + \lambda - {\lambda ^2}\) <strong><em>A1</em></strong></p>
<p>\( = \lambda \) <strong><em>AG</em></strong></p>
<p><strong><em>[6 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(i) \({\text{E}}(S) = 2\lambda - \lambda = \lambda \) <strong><em>A1</em></strong></p>
<p>(ii) \({\text{Var}}(S) = 4\lambda + \lambda = 5\lambda \) <strong><em>(A1)A1</em></strong></p>
<p> </p>
<p><strong>Note: </strong>First <strong><em>A1 </em></strong>can be awarded for either \(4\lambda \) or \(\lambda \).</p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(i) \({\text{E}}(T) = \frac{\lambda }{2} + \frac{\lambda }{2} = \lambda \;\;\;\)(so <em>\(T\) </em>is an unbiased estimator) <strong><em>A1</em></strong></p>
<p>(ii) \({\text{Var}}(T) = \frac{1}{4}\lambda + \frac{1}{4}\lambda = \frac{1}{2}\lambda \) <strong><em>A1</em></strong></p>
<p>this is less than \({\text{Var}}(S)\)<em>, </em>therefore \(T\) is the more efficient estimator <strong><em>R1AG</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Follow through their variances from (b)(ii) and (c)(ii).</p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">no, mean does not equal the variance <span class="Apple-converted-space"> </span><strong><em>R1</em></strong></p>
<p class="p1"><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\({G_{X + Y}}(t) = {e^{\lambda (t - 1)}} \times {e^{\lambda (t - 1)}} = {e^{2\lambda (t - 1)}}\) <span class="Apple-converted-space"> </span><strong><em>M1A1</em></strong></p>
<p class="p1">which is the probability generating function for a Poisson with a mean of \(2\lambda \) <span class="Apple-converted-space"> </span><strong><em>R1AG</em></strong></p>
<p class="p1"><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> </span>\({G_{X + Y}}(1) = 1\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>\({G_{X + Y}}( - 1) = {e^{ - 4\lambda }}\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1"><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\({G_{X + Y}}(1) = p(0) + p(1) + p(2) + p(3) \ldots \)</p>
<p class="p1">\({G_{X + Y}}( - 1) = p(0) - p(1) + p(2) - p(3) \ldots \)</p>
<p class="p1">so \({\text{2P(even)}} = {G_{X + Y}}(1) + {G_{X + Y}}( - 1)\) <span class="Apple-converted-space"> </span><strong><em>(M1)(A1)</em></strong></p>
<p class="p1">\({\text{P(even)}} = \frac{1}{2}(1 + {e^{ - 4\lambda }})\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1"><strong><em>[3 marks]</em></strong></p>
<p class="p1"><strong><em>Total [21 marks]</em></strong></p>
<div class="question_part_label">g.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">Solutions to the different parts of this question proved to be extremely variable in quality with some parts well answered by the majority of the candidates and other parts accessible to only a few candidates. Part (a) was well answered in general although the presentation was sometimes poor with some candidates doing the differentiation of \(G(t)\) and the substitution of \(t = 1\) simultaneously.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Part (b) was well answered in general, the most common error being to state that \({\text{Var}}(2X - Y) = {\text{Var}}(2X) - {\text{Var}}(Y)\).</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Parts (c) and (d) were well answered by the majority of candidates.</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Parts (c) and (d) were well answered by the majority of candidates.</p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Solutions to (e), however, were extremely disappointing with few candidates giving correct solutions. A common incorrect solution was the following:</p>
<p class="p1">\(\;\;\;{G_{X + Y}}(t) = {G_X}(t){G_Y}(t)\)</p>
<p class="p1">Differentiating,</p>
<p class="p1">\(\;\;\;{G'_{X + Y}}(t) = {G'_X}(t){G_Y}(t) + {G_X}(t){G'_Y}(t)\)</p>
<p class="p1">\(\;\;\;{\text{E}}(X + Y) = {G'_{X + Y}}(1) = {\text{E}}(X) \times 1 + {\text{E}}(Y) \times 1 = 2\lambda \)</p>
<p class="p1">This is correct mathematics but it does not show that \(X + Y\) is Poisson and it was given no credit. Even the majority of candidates who showed that \({G_{X + Y}}(t) = {{\text{e}}^{2\lambda (t - 1)}}\) failed to state that this result proved that \(X + Y\) is Poisson and they usually differentiated this function to show that \({\text{E}}(X + Y) = 2\lambda \).</p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">In (f), most candidates stated that \({G_{X + Y}}(1) = 1\) even if they were unable to determine \({G_{X + Y}}(t)\) but many candidates were unable to evaluate \({G_{X + Y}}( - 1)\). Very few correct solutions were seen to (g) even if the candidates correctly evaluated \({G_{X + Y}}(1)\) and \({G_{X + Y}}( - 1)\).</p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">g.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">Engine oil is sold in cans of two capacities, large and small. The amount, in millilitres, in each can, is normally distributed according to Large \( \sim {\text{N}}(5000,{\text{ }}40)\) and Small \( \sim {\text{N}}(1000,{\text{ }}25)\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">A large can is selected at random. Find the probability that the can contains at least \(4995\) millilitres of oil.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">A large can and a small can are selected at random. Find the probability that the large can contains at least \(30\) milliliters more than five times the amount contained in the small can.</p>
<div class="marks">[6]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">A large can and five small cans are selected at random. Find the probability that the large can contains at least \(30\) milliliters less than the total amount contained in the small cans.</p>
<div class="marks">[5]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">\({\text{P}}(L \ge 4995) = 0.785\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>(M1)A1</em></strong></span></p>
<p class="p2"> </p>
<p class="p3"><strong>Note:</strong> <span class="Apple-converted-space"> </span>Accept any answer that rounds correctly to \(0.79\).</p>
<p class="p3">Award <strong><em>M1A0</em></strong> for \(0.78\).</p>
<p class="p2"> </p>
<p class="p3"><strong>Note:</strong> <span class="Apple-converted-space"> </span>Award <strong><em>M1A0</em></strong> for any answer that rounds to \(0.55\) obtained by taking \({\text{SD}} = 40\).</p>
<p class="p3"><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">we are given that \(L \sim {\text{N}}(5000,{\text{ }}40)\) and \(S \sim {\text{N}}(1000,{\text{ }}25)\)</p>
<p class="p1">consider \(X = L - 5S\) <span class="s1">(</span>ignore \( \pm 30\)) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1">\({\text{E}}(X) = 0\) (\( \pm 30\) consistent with line above<span class="s1">) <span class="Apple-converted-space"> </span></span><strong><em>A1</em></strong></p>
<p class="p1">\({\text{Var}}(X) = {\text{Var}}(L) + 25{\text{Var}}(S) = 40 + 625 = 665\) <span class="Apple-converted-space"> </span><strong><em>(M1)A1</em></strong></p>
<p class="p1">require \({\text{P}}(X \ge 30)\;\;\;({\text{or P}}(X \ge 0){\text{ if }} - 30{\text{ above}})\) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1">obtain \(0.122\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note:</strong> <span class="Apple-converted-space"> </span>Accept any answer that rounds correctly to \(2\) significant figures.</p>
<p class="p1"><em><strong>[6 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>consider \(Y = L - ({S_1} + {S_2} + {S_3} + {S_4} + {S_5})\) (ignore \( \pm 30\)) <strong><em>(M1)</em></strong></p>
<p>\({\text{E}}(Y) = 0\) (\( \pm 30\) consistent with line above) <strong><em>A1</em></strong></p>
<p>\({\text{Var}}(Y) = 40 + 5 \times 25 = 165\) <strong><em>A1</em></strong></p>
<p>require \({\text{P}}(Y \le - 30){\text{ (or P}}(Y \le 0){\text{ if }} + 30{\text{ above)}}\) <strong><em>(M1)</em></strong></p>
<p>obtain \(0.00976\) <strong><em>A1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Accept any answer that rounds correctly to \(2\) significant figures.</p>
<p> </p>
<p><strong>Note:</strong> Condone the notation \(Y = L - 5S\) if the variance is correct.</p>
<p style="text-align: left;"><em><strong>[5 marks]</strong></em></p>
<p style="text-align: left;"><em><strong>Total [13 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">Most candidates solved (a) correctly. In (b) and (c), however, many candidates made the usual error of confusing \(\sum\limits_{i = 1}^n {{X_i}} \) and \(nX\)<em>. </em>Indeed some candidates even use the second expression to mean the first. This error leads to an incorrect variance and of course an incorrect answer. Some candidates had difficulty in converting the verbal statements into the correct probability statements, particularly in (c).</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Most candidates solved (a) correctly. In (b) and (c), however, many candidates made the usual error of confusing \(\sum\limits_{i = 1}^n {{X_i}} \) and \(nX\)<em>. </em>Indeed some candidates even use the second expression to mean the first. This error leads to an incorrect variance and of course an incorrect answer. Some candidates had difficulty in converting the verbal statements into the correct probability statements, particularly in (c).</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Most candidates solved (a) correctly. In (b) and (c), however, many candidates made the usual error of confusing \(\sum\limits_{i = 1}^n {{X_i}} \) and \(nX\)<em>. </em>Indeed some candidates even use the second expression to mean the first. This error leads to an incorrect variance and of course an incorrect answer. Some candidates had difficulty in converting the verbal statements into the correct probability statements, particularly in (c).</p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">When Andrew throws a dart at a target, the probability that he hits it is \(\frac{1}{3}\) ; when Bill throws a dart at the target, the probability that he hits the it is \(\frac{1}{4}\) . Successive throws are independent. One evening, they throw darts at the target alternately, starting with Andrew, and stopping as soon as one of their darts hits the target. Let <em>X</em> denote the total number of darts thrown.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Write down the value of \({\text{P}}(X = 1)\) and show that \({\text{P}}(X = 2) = \frac{1}{6}\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Show that the probability generating function for <em>X</em> is given by</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\[G(t) = \frac{{2t + {t^2}}}{{6 - 3{t^2}}}.\]</span></p>
<div class="marks">[6]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Hence determine \({\text{E}}(X)\).</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{P}}(X = 1) = \frac{1}{3}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{P}}(X = 2) = \frac{2}{3} \times \frac{1}{4}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(= \frac{1}{6}\) <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(G(t) = \frac{1}{3}t + \frac{2}{3} \times \frac{1}{4}{t^2} + \frac{2}{3} \times \frac{3}{4} \times \frac{1}{3}{t^3} + \frac{2}{3} \times \frac{3}{4} \times \frac{2}{3} \times \frac{1}{4}{t^4} + \ldots \) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{1}{3}t\left( {1 + \frac{1}{2}{t^2} + \ldots } \right) + \frac{1}{6}{t^2}\left( {1 + \frac{1}{2}{t^2} + \ldots } \right)\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{{\frac{t}{3}}}{{1 - \frac{{{t^2}}}{2}}} + \frac{{\frac{{{t^2}}}{6}}}{{1 - \frac{{{t^2}}}{2}}}\) <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{{2t + {t^2}}}{{6 - 3{t^2}}}\) <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[6 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(G'(t) = \frac{{(2 + 2t)(6 - 3{t^2}) + 6t(2t + {t^2})}}{{{{(6 - 3{t^2})}^2}}}\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{E}}(X) = G'(1) = \frac{{10}}{3}\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[4 marks]</em></strong></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The weights of the oranges produced by a farm may be assumed to be normally distributed with mean 205 grams and standard deviation 10 grams.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find the probability that a randomly chosen orange weighs more than 200 grams.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Five of these oranges are selected at random to be put into a bag. Find the probability that the combined weight of the five oranges is less than 1 kilogram.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The farm also produces lemons whose weights may be assumed to be normally distributed with mean 75 grams and standard deviation 3 grams. Find the probability that the weight of a randomly chosen orange is more than three times the weight of a randomly chosen lemon.</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(z = \frac{{200 - 205}}{{10}} = - 0.5\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">probability = 0.691 (accept 0.692) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;">Note:</strong><span style="font-family: 'times new roman', times; font-size: medium;"> Award </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>M1A0</em></strong><span style="font-family: 'times new roman', times; font-size: medium;"> for 0.309 or 0.308</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"><em> </em></strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">let <em>X</em> be the total weight of the 5 oranges</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">then \({\text{E}}(X) = 5 \times 205 = 1025\) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{Var}}(X) = 5 \times 100 = 500\) <strong><em>(M1)(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{P}}(X < 1000) = 0.132\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[4 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">let <em>Y</em> = <em>B</em> – 3<em>C</em> where <em>B</em> is the weight of a random orange and <em>C</em> the weight of a random lemon <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{E}}(Y) = 205 - 3 \times 75 = - 20\) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{Var}}(Y) = 100 + 9 \times 9 = 181\) <strong><em>(M1)(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{P}}(Y > 0) = 0.0686\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[5 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;">Note:</strong><span style="font-family: 'times new roman', times; font-size: medium;"> Award </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>A1</em></strong><span style="font-family: 'times new roman', times; font-size: medium;"> for 0.0681 obtained from tables</span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">As might be expected, (a) was well answered by many candidates, although those who gave 0.6915 straight from tables were given an arithmetic penalty. Parts (b) and (c), however, were not so well answered with errors in calculating the variances being the most common source of incorrect solutions. In particular, some candidates are still uncertain about the difference between <em>nX</em> and \(\sum\limits_{i = 1}^n {{X_i}} \) .</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">As might be expected, (a) was well answered by many candidates, although those who gave 0.6915 straight from tables were given an arithmetic penalty. Parts (b) and (c), however, were not so well answered with errors in calculating the variances being the most common source of incorrect solutions. In particular, some candidates are still uncertain about the difference between <em>nX</em> and \(\sum\limits_{i = 1}^n {{X_i}} \) .</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">As might be expected, (a) was well answered by many candidates, although those who gave 0.6915 straight from tables were given an arithmetic penalty. Parts (b) and (c), however, were not so well answered with errors in calculating the variances being the most common source of incorrect solutions. In particular, some candidates are still uncertain about the difference between <em>nX</em> and \(\sum\limits_{i = 1}^n {{X_i}} \) .</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Determine the probability generating function for \(X \sim {\text{B}}(1,{\text{ }}p)\).</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Explain why the probability generating function for \({\text{B}}(n,{\text{ }}p)\) is a polynomial of degree \(n\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Two independent random variables \({X_1}\) and \({X_2}\) are such that \({X_1} \sim {\text{B}}(1,{\text{ }}{p_1})\) <span class="s1">and \({X_2} \sim {\text{B}}(1,{\text{ }}{p_2})\)</span>. Prove that if \({X_1} + {X_2}\) has a binomial distribution then \({p_1} = {p_2}\).</p>
<div class="marks">[5]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">\({\text{P}}(X = 0) = 1 - p( = q);{\text{ P}}(X = 1) = p\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>(M1)(A1)</em></strong></span></p>
<p class="p1">\({{\text{G}}_x}(t) = \sum\limits_r {{\text{P}}(X = r){t^r}\;\;\;} \)(or writing out term by term) <span class="Apple-converted-space"> </span><strong><em>M1</em></strong></p>
<p class="p1">\( = q + pt\) <strong><em>A1</em></strong></p>
<p class="p1"><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><strong>METHOD 1</strong></p>
<p class="p1">\(PGF\) for \(B(n,{\text{ }}p)\) is \({(q + pt)^n}\) <span class="Apple-converted-space"> </span><strong><em>R1</em></strong></p>
<p class="p1">which is a polynomial of degree \(n\) <span class="Apple-converted-space"> </span><strong><em>R1</em></strong></p>
<p class="p1"><strong>METHOD 2</strong></p>
<p class="p1">in \(n\) independent trials, it is not possible to obtain more than \(n\) succes<span class="s1">ses (or equivalent, <em>eg</em>, \({\text{P}}(X > n) = 0\)) <span class="Apple-converted-space"> </span></span><strong><em>R1</em></strong></p>
<p class="p1">so \({a_r} = 0\) for \(r > n\) <span class="Apple-converted-space"> </span><strong><em>R1</em></strong></p>
<p class="p1"><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">let \(Y = {X_1} + {X_2}\)</p>
<p class="p1">\({G_Y}(t) = ({q_1} + {p_1}t)({q_2} + {p_2}t)\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">\({G_Y}(t)\) has degree two, so if \(Y\) is binomial then</p>
<p class="p1">\(Y \sim {\text{B}}(2,{\text{ }}p)\) for some \(p\) <span class="Apple-converted-space"> </span><strong><em>R1</em></strong></p>
<p class="p1">\({(q + pt)^2} = ({q_1} + {p_1}t)({q_2} + {p_2}t)\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note:</strong> <span class="Apple-converted-space"> </span>The \(LHS\) could be seen as \({q^2} + 2pqt + {p^2}{t^2}\).</p>
<p class="p2"> </p>
<p class="p1"><strong>METHOD 1</strong></p>
<p class="p1">by considering the roots of both sides, \(\frac{{{q_1}}}{{{p_1}}} = \frac{{{q_2}}}{{{p_2}}}\) <span class="Apple-converted-space"> </span><strong><em>M1</em></strong></p>
<p class="p1">\(\frac{{1 - {p_1}}}{{{p_1}}} = \frac{{1 - {p_2}}}{{{p_2}}}\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">so \({p_1} = {p_2}\) <span class="Apple-converted-space"> </span><strong><em>AG</em></strong></p>
<p class="p1"><strong>METHOD 2</strong></p>
<p class="p1">equating coefficients,</p>
<p class="p1">\({p_1}{p_2} = {p^2},{\text{ }}{q_1}{q_2} = {q^2}{\text{ or }}(1 - {p_1})(1 - {p_2}) = {(1 - p)^2}\) <span class="Apple-converted-space"> </span><strong><em>M1</em></strong></p>
<p class="p1">expanding,</p>
<p class="p1">\({p_1} + {p_2} = 2p\) so \({p_1},{\text{ }}{p_2}\) are the roots of \({x^2} - 2px + {p^2} = 0\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">so \({p_1} = {p_2}\) <span class="Apple-converted-space"> </span><strong><em>AG</em></strong></p>
<p class="p1"><strong><em>[5 marks]</em></strong></p>
<p class="p1"><strong><em>Total [11 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">Solutions to (a) were often disappointing with some candidates simply writing down the answer. A common error was to forget the possibility of \(X\) being zero so that \(G(t) = pt\) was often seen.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Explanations in (b) were often poor, again indicating a lack of ability to give a verbal explanation.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Very few complete solutions to (c) were seen with few candidates even reaching the result that \(({q_1} + {p_1}t)({q_2} + {p_2}t)\) must equal \({(q + pt)^2}\) for some \(p\).</p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The random variable <em>X</em> is assumed to have probability density function <em>f</em>, where</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\[f(x) = \left\{ {\begin{array}{*{20}{c}}<br> {\frac{x}{{18,}}}&{0 \leqslant x \leqslant 6} \\ <br> {0,}&{{\text{otherwise}}{\text{.}}} <br>\end{array}} \right.\]</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Show that if the assumption is correct, then</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\[{\text{P}}(a \leqslant X \leqslant b) = \frac{{{b^2} - {a^2}}}{{36}},{\text{ for }}0 \leqslant a \leqslant b \leqslant 6.\]</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{P}}(a \leqslant X \leqslant b) = \int_a^b {\frac{x}{{18}}{\text{d}}x} \) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \left[ {\frac{{{x^2}}}{{36}}} \right]_a^b\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{{{b^2} - {a^2}}}{{36}}\) <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[3 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">This was the best answered question on the paper, helped probably by the fact that rounding errors in finding the expected frequencies were not an issue. In (a), some candidates thought, incorrectly, that all they had to do was to show that \(\int_0^6 {f(x){\text{d}}x = 1} \).</span></p>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The discrete random variable <em>X</em> has the following probability distribution, where \(0 < \theta < \frac{1}{3}\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="font: normal normal normal 23px/normal Helvetica; text-align: center; margin: 0px;"><img src="data:image/png;base64,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" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Determine \({\text{E}}(X)\) and show that \({\text{Var}}(X) = 6\theta - 16{\theta ^2}\).</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">In order to estimate \(\theta \), a random sample of <em>n</em> observations is obtained from the distribution of <em>X</em> .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) Given that \({\bar X}\) denotes the mean of this sample, show that</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\[{{\hat \theta }_1} = \frac{{3 - \bar X}}{4}\]</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">is an unbiased estimator for \(\theta \) and write down an expression for the variance of \({{\hat \theta }_1}\) in terms of <em>n</em> and \(\theta \).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) Let <em>Y</em> denote the number of observations that are equal to 1 in the sample. Show that <em>Y</em> has the binomial distribution \({\text{B}}(n,{\text{ }}\theta )\) and deduce that \({{\hat \theta }_2} = \frac{Y}{n}\) is another unbiased estimator for \(\theta \). Obtain an expression for the variance of \({{\hat \theta }_2}\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(iii) Show that \({\text{Var}}({{\hat \theta }_1}) < {\text{Var}}({{\hat \theta }_2})\) and state, with a reason, which is the more </span><span style="font-family: 'times new roman', times; font-size: medium;">efficient estimator, \({{\hat \theta }_1}\) or \({{\hat \theta }_2}\).</span></p>
<div class="marks">[10]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{E}}(X) = 1 \times \theta + 2 \times 2\theta + 3(1 - 3\theta ) = 3 - 4\theta \) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{Var}}(X) = 1 \times \theta + 4 \times 2\theta + 9(1 - 3\theta ) - {(3 - 4\theta )^2}\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = 6\theta - 16{\theta ^2}\) <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[4 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) \({\text{E}}({\hat \theta _1}) = \frac{{3 - {\text{E}}(\bar X)}}{4} = \frac{{3 - (3 - 4\theta )}}{4} = \theta \) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">so \({\hat \theta _1}\) is an unbiased estimator of \(\theta \) <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{Var}}({{\hat \theta }_1}) = \frac{{6\theta - 16{\theta ^2}}}{{16n}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) each of the <em>n</em> observed values has a probability \(\theta \) of having the value 1 <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">so \(Y \sim {\text{B}}(n,{\text{ }}\theta )\) <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{E}}({{\hat \theta }_2}) = \frac{{{\text{E}}(Y)}}{n} = \frac{{n\theta }}{n} = \theta \) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{Var}}({{\hat \theta }_2}) = \frac{{n\theta (1 - \theta )}}{{{n^2}}} = \frac{{\theta (1 - \theta )}}{n}\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(iii) \({\text{Var}}({{\hat \theta }_1}) - {\text{Var}}({{\hat \theta }_2}) = \frac{{6\theta - 16{\theta ^2} - 16\theta + 16{\theta ^2}}}{{16n}}\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{{ - 10\theta }}{{16n}} < 0\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({{\hat \theta }_1}\) is the more efficient estimator since it has the smaller variance <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"><em>[10 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Bill also has a box with 10 biscuits in it. 4 biscuits are chocolate and 6 are plain. Bill takes a biscuit from his box at random, looks at it and replaces it in the box. He repeats this process until he has looked at 5 biscuits in total. Let <em>B </em>be the number of chocolate biscuits that Bill takes and looks at.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">State the distribution of <em>B </em>.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Find P(<em>B </em>= 3) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 36.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Find P(<em>B </em>= 5) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><em>B </em>has the binomial distribution \(\left( {B\left( {5,\frac{4}{{10}}} \right)} \right)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[1 mark]</em></strong></span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{P}}(B = 3) = \left( {\left( {\begin{array}{*{20}{c}}<br> 5 \\ <br> 3 <br>\end{array}} \right){{\left( {\frac{4}{{10}}} \right)}^3}{{\left( {\frac{6}{{10}}} \right)}^2} = } \right)\frac{{144}}{{625}}( = 0.2304)\) <strong><em>(M1)A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;">Note</strong><span style="font-family: 'times new roman', times; font-size: medium;">: Accept 0.230.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"><em> </em></strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"><em>[2 marks]</em></strong></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{P}}(B = 5) = \left( {{{\left( {\frac{4}{{10}}} \right)}^5} = } \right)\frac{{32}}{{3125}}( = 0.01024)\) <strong><em>(M1)A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;">Note</strong><span style="font-family: 'times new roman', times; font-size: medium;">: Accept 0.0102.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"><em> </em></strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"><em>[2 marks]</em></strong></p>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">This was generally well answered. Some students did not read the question carefully enough and see the comparisons made between the Hypergeometric distribution and the Binomial distribution, with 5 trials (some candidates went to 10 trials) in each case. Part (h) caused the most problems and it was very rare to see a script that gained the reasoning mark for saying that <em>A </em>and <em>B </em>were independent events. This question was a good indicator of the standard of the rest of the paper.</span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">This was generally well answered. Some students did not read the question carefully enough and see the comparisons made between the Hypergeometric distribution and the Binomial distribution, with 5 trials (some candidates went to 10 trials) in each case. Part (h) caused the most problems and it was very rare to see a script that gained the reasoning mark for saying that <em>A </em>and <em>B </em>were independent events. This question was a good indicator of the standard of the rest of the paper.</span></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">This was generally well answered. Some students did not read the question carefully enough and see the comparisons made between the Hypergeometric distribution and the Binomial distribution, with 5 trials (some candidates went to 10 trials) in each case. Part (h) caused the most problems and it was very rare to see a script that gained the reasoning mark for saying that <em>A </em>and <em>B </em>were independent events. This question was a good indicator of the standard of the rest of the paper.</span></p>
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">The random variable <em>X </em>has probability distribution Po(8).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) Find \({\text{P}}(X = 6)\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) Find \({\text{P}}(X = 6|5 \leqslant X \leqslant 8)\).</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\bar X\) denotes the sample mean of \(n > 1\) independent observations from \(X\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) Write down \({\text{E}}(\bar X)\) and \({\text{Var}}(\bar X)\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) Hence, give a reason why \(\bar X\) is not a Poisson distribution.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">A random sample of \(40\) observations is taken from the distribution for \(X\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">(i) Find \({\text{P}}(7.1 < \bar X < 8.5)\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) Given that \({\text{P}}\left( {\left| {\bar X - 8} \right| \leqslant k} \right) = 0.95\), find the value of \(k\).</span></p>
<div class="marks">[6]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) \({\text{P}}(X = 6) = 0.122\) <strong><em>(M1)A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) \({\text{P}}(X = 6|5 \leqslant X \leqslant 8) = \frac{{{\text{P}}(X = 6)}}{{{\text{P}}(5 \leqslant X \leqslant 8)}} = \frac{{0.122 \ldots }}{{0.592 \ldots - 0.0996 \ldots }}\) <strong><em>(M1)(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = 0.248\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[5 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) \({\text{E}}(\bar X) = 8\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{Var}}(\bar X) = \frac{8}{n}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) \({\text{E}}(\bar X) \ne {\text{Var}}(\bar X)\) \({\text{(for }}n > 1)\) <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Times; min-height: 24.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: </strong>Only award the <strong><em>R1 </em></strong>if the two expressions in (b)(i) are different.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Times; min-height: 24.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[3 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) <strong>EITHER</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\bar X \sim {\text{N(8, 0.2)}}\) <strong><em>(M1)A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Times; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: <em>M1 </em></strong>for normality, <strong><em>A1 </em></strong>for parameters.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Times; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{P}}(7.1 < \bar X < 8.5) = 0.846\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>OR</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The expression is equivalent to</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{P}}(283 \leqslant \sum {X \leqslant 339)} \) where \(\sum X \) is \({\text{Po(320)}}\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = 0.840\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Times; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: </strong>Accept 284, 340 instead of 283, 339</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"> Accept any answer that rounds correctly to 0.84 or 0.85.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Times; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) <strong>EITHER</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(k = 1.96\frac{\sigma }{{\sqrt n }}\) or \(1.96{\text{ std}}(\bar X)\) <strong><em>(M1)(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(k = 0.877\) or \(1.96\sqrt {0.2} \) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>OR</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The expression is equivalent to</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(P(320 - 40k \leqslant \sum {X \leqslant 320 + 40k) = 0.95} \) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(k = 0.875\) <strong><em>A2</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Times; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: </strong>Accept any answer that rounds to 0.87 or 0.88.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"> Award <strong><em>M1A0 </em></strong>if modulus sign ignored and answer obtained rounds to 0.74 or 0.75</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Times; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[6 marks]</em></strong></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">The continuous random variable <em>X </em>has probability density function <em>f </em>given by</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\[f(x) = \left\{ {\begin{array}{*{20}{c}}<br> {2x,}&{0 \leqslant x \leqslant 0.5,} \\ <br> {\frac{4}{3} - \frac{2}{3}x,}&{0.5 \leqslant x \leqslant 2} \\ <br> {0,}&{{\text{otherwise}}{\text{.}}} <br>\end{array}} \right.\]</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Sketch the function <em>f </em>and show that the lower quartile is 0.5.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) Determine E(<em>X </em>).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) Determine \({\text{E}}({X^2})\).</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Two independent observations are made from <em>X </em>and the values are added.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">The resulting random variable is denoted <em>Y </em>.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) Determine \({\text{E}}(Y - 2X)\) .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) Determine \({\text{Var}}\,(Y - 2X)\).</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) Find the cumulative distribution function for <em>X </em>.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) Hence, or otherwise, find the median of the distribution.</span></p>
<div class="marks">[7]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">piecewise linear graph</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><br><img src="data:image/png;base64,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" alt></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">correct shape <strong><em>A1<br></em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">with vertices (0, 0), (0.5, 1) and (2, 0) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">LQ: <em>x</em> = 0.5 , because the area of the triangle is 0.25 <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><strong><em><span style="font-family: 'times new roman', times; font-size: medium;">[3 marks]</span><br></em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) \({\text{E}}(X) = \int_0^{0.5} {x \times 2x{\text{d}}x + \int_{0.5}^2 {x \times \left( {\frac{4}{3} - \frac{2}{3}x} \right){\text{d}}x = \frac{5}{6}{\text{ }}( = 0.833...)} } \) <strong><em>(M1)A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) \({\text{E}}({X^2}) = \int_0^{0.5} {{x^2} \times 2x{\text{d}}x + \int_{0.5}^2 {{x^2} \times \left( {\frac{4}{3} - \frac{2}{3}x} \right){\text{d}}x = \frac{7}{8}{\text{ }}( = 0.875)} } \) <strong><em>(M1)A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><strong><em><span style="font-family: 'times new roman', times; font-size: medium;">[4 marks]</span><br></em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) \({\text{E}}(Y - 2X) = 2{\text{E}}(X) - 2{\text{E}}(X) = 0\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) \({\text{Var}}\,(X) = \left( {{\text{E}}({X^2}) - {\text{E}}{{(X)}^2}} \right) = \frac{{13}}{{72}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(Y = {X_1} + {X_2} \Rightarrow {\text{Var}}\,(Y) = 2{\text{Var }}(X)\) <strong> <em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{Var}}\,(Y - 2X) = 2{\text{Var}}\,(X) + 4{\text{Var}}\,(X) = \frac{{13}}{{12}}\) <strong> <em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><strong><em><span style="font-family: 'times new roman', times; font-size: medium;">[5 marks]</span><br></em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) attempt to use \(cf(x) = \int {f(u){\text{d}}u} \) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">obtain \(cf(x) = \left\{ {\begin{array}{*{20}{c}}<br> {{x^2},}&{0 \leqslant x \leqslant 0.5,} \\ <br> {\frac{{4x}}{3} - \frac{1}{3}{x^2} - \frac{1}{3},}&{0.5 \leqslant x \leqslant 2,} <br>\end{array}} \right.\) \(\begin{array}{*{20}{c}}<br> {{\boldsymbol{A1}}} \\ <br> {{\boldsymbol{A2}}} <br>\end{array}\)<br></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) attempt to solve \(cf(x) = 0.5\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{4x}}{3} - \frac{1}{3}{x^2} - \frac{1}{3} = 0.5\) <strong> <em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">obtain 0.775 <strong><em>A1</em></strong></span><strong style="font-family: 'times new roman', times; font-size: medium;"> </strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong> </strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: </strong>Accept attempts in the form of an integral with upper limit the unknown median.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: </strong>Accept exact answer \(2 - \sqrt {1.5} \) .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><strong><em><span style="font-family: 'times new roman', times; font-size: medium;">[7 marks]</span><br></em></strong></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">There was a curious issue about the lower quartile in part (a): The LQ coincides with a quarter of the range of the distribution \(\frac{2}{4} = 0.5\). Sadly this is wrong reasoning – the correct reasoning involves a consideration of areas.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">There was a curious issue about the lower quartile in part (a): The LQ coincides with a quarter of the range of the distribution \(\frac{2}{4} = 0.5\). Sadly this is wrong reasoning – the correct reasoning involves a consideration of areas.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">In part (b) many candidates used hand calculation rather than their GDC.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">The random variable Y was not well understood, and that followed into incorrect calculations involving Y – 2X.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">There was a curious issue about the lower quartile in part (a): The LQ coincides with a quarter of the range of the distribution \(\frac{2}{4} = 0.5\). Sadly this is wrong reasoning – the correct reasoning involves a consideration of areas.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">In part (b) many candidates used hand calculation rather than their GDC.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">The random variable Y was not well understood, and that followed into incorrect calculations involving Y – 2X.</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">There was a curious issue about the lower quartile in part (a): The LQ coincides with a quarter of the range of the distribution \(\frac{2}{4} = 0.5\). Sadly this is wrong reasoning – the correct reasoning involves a consideration of areas.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">In part (b) many candidates used hand calculation rather than their GDC.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">The random variable Y was not well understood, and that followed into incorrect calculations involving Y – 2X.</span></p>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">A random variable \(X\) has probability density function</p>
<p class="p1">\(f(x) = \left\{ {\begin{array}{*{20}{c}} 0&{x < 0} \\ {\frac{1}{2}}&{0 \le x < 1} \\ {\frac{1}{4}}&{1 \le x < 3} \\ 0&{x \ge 3} \end{array}} \right.\)</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch the graph of \(y = f(x)\).</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the cumulative distribution function for \(X\).</p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the interquartile range for \(X\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="Apple-converted-space"><img 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" alt> </span><strong><em>A1</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Ignore open / closed endpoints and vertical lines.</p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>A1 </em></strong>for a correct graph with scales on both axes and a clear indication of the relevant values.</p>
<p class="p1"><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(F(x) = \left\{ {\begin{array}{*{20}{c}} 0&{x < 0} \\ {\frac{x}{2}}&{0 \le x < 1} \\ {\frac{x}{4} + \frac{1}{4}}&{1 \le x < 3} \\ 1&{x \ge 3} \end{array}} \right.\)</p>
<p class="p1">considering the areas in their sketch or using integration <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1">\(F(x) = 0,{\text{ }}x < 0,{\text{ }}F(x) = 1,{\text{ }}x \ge 3\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">\(F(x) = \frac{x}{2},{\text{ }}0 \le x < 1\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">\(F(x) = \frac{x}{4} + \frac{1}{4},{\text{ }}1 \le x < 3\) <span class="Apple-converted-space"> </span><strong><em>A1A1</em></strong></p>
<p class="p1"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Accept \( < \) for \( \le \) in all places and also \( > \) for \( \ge \) first <strong><em>A1</em></strong>.</p>
<p class="p1"><em><strong>[5 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\({Q_3} = 2,{\text{ }}{Q_1} = 0.5\) <span class="Apple-converted-space"> </span><strong><em>A1A1</em></strong></p>
<p class="p1">\({\text{IQR is }}2 - 0.5 = 1.5\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1"><strong><em>[3 marks]</em></strong></p>
<p class="p1"><strong><em>Total [9 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">Part (a) was correctly answered by most candidates. Some graphs were difficult to mark because candidates drew their lines on top of the ruled lines in the answer book. Candidates should be advised not to do this. Candidates should also be aware that the command term ‘sketch’ requires relevant values to be indicated.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">In (b), most candidates realised that the cumulative distribution function had to be found by integration but the limits were sometimes incorrect.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">In (c), candidates who found the upper and lower quartiles correctly sometimes gave the interquartile range as \([0.5,{\text{ }}2]\). It is important for candidates to realise that that the word range has a different meaning in statistics compared with other branches of mathematics.</p>
<div class="question_part_label">c.</div>
</div>
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