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class="breadcrumb"> <li><a href="../../../mathsapplications.html"><i class="fa fa-home"></i></a><i class="fa fa-fw fa-chevron-right divider"></i></li><li><a href="../1065/statistics-and-probability.html">Statistics and Probability</a><i class="fa fa-fw fa-chevron-right divider"></i></li><li><span class="gray">4.7 Discrete random variables</span></li> <span class="pull-right" style="color: #555" title="Suggested study time: 30 minutes"><i class="fa fa-clock-o"></i> 30'</span> </ol> <article id="main-article"> <div class="intro-card"> <div class="bg-cover" style="background-image: url('');"><img alt="" src="../../crowds-1.png" style="width: 137px; height: 137px;"></div> <p><img src="" style="display: none">Random variables are a set of possible outcomes from a random experiment. They can either be discrete or continuous. In this chapter we will find out more about discrete random variables, how they can be represented, displayed and analysed. </p> </div> <div class="panel panel-has-colored-body panel-turquoise"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Key Concepts</p> </div> </div> <div class="panel-body"> <p><span id="docs-internal-guid-6a37b49f-7fff-1af3-1e92-66b35ae8338d"></span></p> <p dir="ltr"><span id="docs-internal-guid-6a37b49f-7fff-1af3-1e92-66b35ae8338d">In this unit you should learn to…</span></p> <ul style="list-style-type:disc;"> <li role="presentation">Understand what a discrete random variable is</li> <li role="presentation">Find the probability distribution of a discrete random variable</li> <li role="presentation">Find the expected value for discrete data</li> </ul> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-yellow"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Essentials</p> </div> </div> <div class="panel-body"> <div> <div class="panel panel-has-colored-body panel-yellow"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>1. Introduction</p> </div> </div> <div class="panel-body"> <div> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/459708398"></iframe></div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-yellow panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>2. Discrete Random Probability</p> </div> </div> <div class="panel-body"> <div> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/459711831"></iframe></div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-yellow panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>3. Expected Value</p> </div> </div> <div class="panel-body"> <div> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/459724783"></iframe></div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-violet"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Summary</p> </div> </div> <div class="panel-body"> <div> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden"> <ul class="gallery layout-row thumb48"><li class=""><a href="../../../std-galleries/15-218/drv1.png" data-fancybox="gallery-218" class="fancy"><img src="../../../std-galleries/15-218/drv1-thumb128.jpg" class="thumb"></a></li><li class=""><a href="../../../std-galleries/15-218/drv2.png" data-fancybox="gallery-218" class="fancy"><img src="../../../std-galleries/15-218/drv2-thumb128.jpg" class="thumb"></a></li><li class=""><a href="../../../std-galleries/15-218/drv3.png" data-fancybox="gallery-218" class="fancy"><img src="../../../std-galleries/15-218/drv3-thumb128.jpg" class="thumb"></a></li><li class=""><a href="../../../std-galleries/15-218/drv4.png" data-fancybox="gallery-218" class="fancy"><img src="../../../std-galleries/15-218/drv4-thumb128.jpg" class="thumb"></a></li><li class=""><a href="../../../std-galleries/15-218/drv5.png" data-fancybox="gallery-218" class="fancy"><img src="../../../std-galleries/15-218/drv5-thumb128.jpg" class="thumb"></a></li><li class=""><a href="../../../std-galleries/15-218/drv6.png" data-fancybox="gallery-218" class="fancy"><img src="../../../std-galleries/15-218/drv6-thumb128.jpg" class="thumb"></a></li><li class=""><a href="../../../std-galleries/15-218/drv7.png" data-fancybox="gallery-218" class="fancy"><img src="../../../std-galleries/15-218/drv7-thumb128.jpg" class="thumb"></a></li><li class=""><a href="../../../std-galleries/15-218/drv8.png" data-fancybox="gallery-218" class="fancy"><img src="../../../std-galleries/15-218/drv8-thumb128.jpg" class="thumb"></a></li><li class=""><a href="../../../std-galleries/15-218/drv9.png" data-fancybox="gallery-218" class="fancy"><img src="../../../std-galleries/15-218/drv9-thumb128.jpg" class="thumb"></a></li><li class=""><a href="../../../std-galleries/15-218/drv10.png" data-fancybox="gallery-218" class="fancy"><img src="../../../std-galleries/15-218/drv10-thumb128.jpg" class="thumb"></a></li><li class=""><a href="../../../std-galleries/15-218/drv11.png" data-fancybox="gallery-218" class="fancy"><img src="../../../std-galleries/15-218/drv11-thumb128.jpg" class="thumb"></a></li><li><a href="../../../std-galleries/15-218/drv12.png" data-fancybox="gallery-218" class="fancy"><img src="../../../std-galleries/15-218/drv12-thumb128.jpg" class="thumb"></a></li></ul> </section> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-green"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Test Yourself</p> </div> </div> <div class="panel-body"> <div> <p>Self Checking quiz</p> <p>Practice your understanding on these quiz questions. Check your answers when you are done and read the worked solutions when you get stuck. If you find there are still some gaps in your understanding then go back to the videos above<em>.</em></p> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden"> <div class="tib-quiz" data-stats="15-521-2190"><div class="label label-default q-number">1</div><div class="exercise shadow-bottom"><div class="q-question"><p>The following table shows the probability distribution of a discrete random variable X.</p><table border="0" cellpadding="0" cellspacing="0" height="45" width="277"><tbody><tr><td>X</td><td>1</td><td>2</td><td>3</td><td>4</td></tr><tr><td>P(X=x)</td><td>0.2</td><td>0.3</td><td> x </td><td>0.4</td></tr></tbody></table><p>Find the value of x.</p></div><div class="q-answer"><p><input type="text" style="height: auto;" data-c="0.1"> <span class="review"></span> </p></div><div class="q-explanation"><p>The sum of probabilities in a probability distribution must be one (i.e. 100%). Therefore, 0.2+0.3+x+0.1=1 and so x=0.1.</p></div><div class="remove-section" style="display: none;" title="Remove question field"> </div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="label label-default q-number">2</div><div class="exercise shadow-bottom"><div class="q-question"><p>The following table shows the probability distribution of a discrete random variable X.</p><table border="0" cellpadding="0" cellspacing="0" height="45" width="277"><tbody><tr><td>X</td><td>1</td><td>2</td><td>3</td><td>4</td></tr><tr><td>P(X=x)</td><td>0.3</td><td>0.4</td><td>0.2</td><td>0.1</td></tr></tbody></table><p>Find E(X).</p></div><div class="q-answer"><p><input type="text" style="height: auto;" data-c="2.1"> <span class="review"></span></p></div><div class="q-explanation"><p>To find the expected value, E(X): <span class="math-tex">\(1\times0.3+2\times0.4+3\times0.2+4\times0.1=2.1\)</span></p></div><div class="remove-section" style="display: none;" title="Remove question field"> </div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="label label-default q-number">3</div><div class="exercise shadow-bottom"><div class="q-question"><p>Which of the following are examples of discrete random variables?</p></div><div class="q-answer"><p><label class="checkbox"><input type="checkbox"> The lengths of leaves on a tree. </label></p><p><label class="checkbox"><input class="c" type="checkbox"> Marks on a test out of 10.</label></p><p><label class="checkbox"><input class="c" type="checkbox"> The score on a die.</label></p><p><label class="checkbox"><input type="checkbox"> The heights of students in a school.</label></p></div><div class="q-explanation"><p>Discrete random variables can only take a countable number of values. The marks on a test and the score on a die are both countable and so they are discrete random variables. In contrast, lengths of leaves and heights of students are measured, and they can take an infinite number of values. They are not discrete random variables.</p></div><div class="remove-section" style="display: none;" title="Remove question field"> </div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="label label-default q-number">4</div><div class="exercise shadow-bottom"><div class="q-question"><p>X is a discrete random variable. Find the value of k in the following probability distribution.</p><table border="0" cellpadding="0" cellspacing="0" height="45" width="233"><tbody><tr><td>X</td><td>1</td><td>2</td><td>3</td></tr><tr><td>P(X=X)</td><td>k </td><td>2k</td><td>3k</td></tr></tbody></table><p>Leave your answer as a fraction (use a / between the numerator and denominator)</p></div><div class="q-answer"><p> <input type="text" style="height: auto;" data-c="1/6"> <span class="review"></span> </p></div><div class="q-explanation"><p>The sum of probabilities in a probability distribution must be one (i.e. 100%). Therefore, <span class="math-tex">\(k+2k+3k=1\)</span> and so <span class="math-tex">\(6k=1\)</span>, which means <span class="math-tex">\(k=\frac{1}{6}\)</span>.</p></div><div class="remove-section" style="display: none;" title="Remove question field"> </div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="label label-default q-number">5</div><div class="exercise shadow-bottom"><div class="q-question"><p>The following table shows the probability distribution of a discrete random variable, A.</p><table border="0" cellpadding="0" cellspacing="0" height="45" width="452"><tbody><tr><td>a</td><td>2 </td><td>3</td><td>4</td><td>5 </td></tr><tr><td>P(A=a)</td><td>x</td><td>y </td><td>0.1</td><td>0.2</td></tr></tbody></table><p>Given that E(A) = 3.4, find the value of x and y.</p></div><div class="q-answer"><p>x = <input type="text" style="height: auto;" data-c="0.1"> <span class="review"></span></p><p>y = <input type="text" style="height: auto;" data-c="0.6"> <span class="review"></span></p></div><div class="q-explanation"><p>Given that we have two unknowns, we will create 2 simultneous equations to solve.</p><p>Equation 1: <span class="math-tex">\(x+y+0.2+0.1=1\)</span>, and thus <span class="math-tex">\(x+y=0.7\)</span></p><p>Equation 2: <span class="math-tex">\(2\times x+3\times y+4 \times 0.1+5\times 0.2=3.4\)</span>, and thus <span class="math-tex">\(2x+3y=2\)</span></p><p>Solving these linear simultaneous equations on the GDC, we obtain <span class="math-tex">\(x=0.1\)</span> and <span class="math-tex">\(y=0.6\)</span>.</p></div><div class="remove-section" style="display: none;" title="Remove question field"> </div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="label label-default q-number">6</div><div class="exercise shadow-bottom"><div class="q-question"><p>Based on last season's statistics, a football player has the following probability distribution for goal scoring, with the discrete random variable, Y, representing the number of goals per game. </p><table border="0" cellpadding="0" cellspacing="0" height="45" width="312"><tbody><tr><td>y</td><td>0</td><td>1</td><td>2</td><td>3</td></tr><tr><td>P(Y=y)</td><td>0.3</td><td>0.45</td><td>0.2</td><td>0.05</td></tr></tbody></table><p>Find the expected number of goals he will score in the next game. Leave your answer to the nearest positive integer.</p></div><div class="q-answer"><p> <input type="text" style="height: auto;" data-c="1"> <span class="review"></span> </p></div><div class="q-explanation"><p>The expected value, <span class="math-tex">\(E(X)=0\times0.3+1\times0.45+2\times0.2+3\times0.05=1 \)</span>.</p></div><div class="remove-section" style="display: none;" title="Remove question field"> </div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="label label-default q-number">7</div><div class="exercise shadow-bottom"><div class="q-question"><p>The random variable <span class="math-tex">\(X\)</span> has a probability distribution given by the function, <span class="math-tex">\(P(X=x)=\frac{2x}{k}, x=1,2,3\)</span>.</p><p>Find the value of the constant, <span class="math-tex">\(k\)</span>.</p></div><div class="q-answer"><p><label class="radio"><input class="c" type="radio"> 12</label></p><p><label class="radio"><input type="radio"> 1</label></p><p><label class="radio"><input type="radio"> 6</label></p><p><label class="radio"><input type="radio"> 10</label></p></div><div class="q-explanation"><p>If we substitute the given values of <span class="math-tex">\(x \)</span> into the function, we obtain the following table:</p><table border="0" cellpadding="0" cellspacing="0" height="45" width="168"><tbody><tr><td><span class="math-tex">\(x \)</span></td><td>1 </td><td>2 </td><td>3 </td></tr><tr><td><span class="math-tex">\(P(X=x)\)</span></td><td><span class="math-tex">\(\frac{2}{k}\)</span></td><td><span class="math-tex">\(\frac{4}{k}\)</span></td><td><span class="math-tex">\(\frac{6}{k}\)</span></td></tr></tbody></table><p>Since the probabilities in a probability distribution add up to one, then <span class="math-tex">\(\frac{2}{k}+\frac{4}{k}+\frac{6}{k}=1\)</span>, so that <span class="math-tex">\(\frac{12}{k}=1\)</span> and hence <span class="math-tex">\(k=12\)</span>.</p></div><div class="remove-section" style="display: none;" title="Remove question field"> </div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="label label-default q-number">8</div><div class="exercise shadow-bottom"><div class="q-question"><p>A survey was taken in a school asking how many hours, to the nearest hour, IB Diploma students studied for each night. Relative frequencies were calculated, and the table below shows the probability distribution. The random variable, X, is how many hours per night students study for.</p><table border="0" cellpadding="0" cellspacing="0" style="width:100%;"><tbody><tr><td><span class="math-tex">\(x \)</span></td><td>0</td><td>1</td><td>2</td><td>3</td></tr><tr><td><span class="math-tex">\(P(X=x)\)</span></td><td>0.05</td><td>0.3</td><td>0.5</td><td>0.15</td></tr></tbody></table><p>Find <span class="math-tex">\(P\left(2\le X\le3\right)\)</span>.</p></div><div class="q-answer"><p><label class="radio"><input class="c" type="radio"> 0.65</label></p><p><label class="radio"><input type="radio"> 0.3</label></p><p><label class="radio"><input type="radio"> 0.8</label></p><p><label class="radio"><input type="radio"> 0.35</label></p></div><div class="q-explanation"><p><span class="math-tex">\(P\left(2\le X\le3\right)\)</span> is the probability that a student studies between 2 and 3 hours a night, including those values. That is 0.5 + 0.15 = 0.65.</p></div><div class="remove-section" style="display: none;" title="Remove question field"> </div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="label label-default q-number">9</div><div class="exercise shadow-bottom"><div class="q-question"><p>The following table shows the probability distribution of a discrete random variable, A.</p><table border="0" cellpadding="0" cellspacing="0" height="45" width="452"><tbody><tr><td>a</td><td>2 </td><td>3</td><td>4</td><td>5 </td></tr><tr><td>P(A=a)</td><td>x</td><td>0.2 </td><td>y</td><td>0.2</td></tr></tbody></table><p>Given that E(A) = 3.8, find the value of x and y.</p></div><div class="q-answer"><p>x = <input type="text" style="height: auto;" data-c="0.1"> <span class="review"></span></p><p>y = <input type="text" style="height: auto;" data-c="0.5"> <span class="review"></span></p></div><div class="q-explanation"><p>Given that we have two unknowns, we will create 2 simultaneous equations to solve.</p><p>Equation 1: <span class="math-tex">\(x+0.2+y+0.2=1\)</span>, and thus <span class="math-tex">\(x+y=0.6\)</span></p><p>Equation 2: <span class="math-tex">\(2\times x+3\times 0.2+4 \times y+5\times 0.2=3.8\)</span>, and thus <span class="math-tex">\(2x+4y=2.2\)</span></p><p>Solving these linear simultaneous equations on the GDC, we obtain <span class="math-tex">\(x=0.1\)</span> and <span class="math-tex">\(y=0.5\)</span>.</p></div><div class="remove-section" style="display: none;" title="Remove question field"> </div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="label label-default q-number">10</div><div class="exercise shadow-bottom"><div class="q-question"><p>The following table shows the probability distribution of a discrete random variable, A.</p><table border="0" cellpadding="0" cellspacing="0" height="45" width="452"><tbody><tr><td>a</td><td>2 </td><td>3</td><td>4</td><td>5 </td></tr><tr><td>P(A=a)</td><td>0.3</td><td>x</td><td>y</td><td>0.2</td></tr></tbody></table><p>Given that E(A) = 3.4, find the value of x and y.</p></div><div class="q-answer"><p>x = <input type="text" style="height: auto;" data-c="0.2"> <span class="review"></span></p><p>y = <input type="text" style="height: auto;" data-c="0.3"> <span class="review"></span></p></div><div class="q-explanation"><p>Given that we have two unknowns, we will create 2 simultaneous equations to solve.</p><p>Equation 1: <span class="math-tex">\(0.3+x+y+0.2=1\)</span>, and thus <span class="math-tex">\(x+y=0.5\)</span></p><p>Equation 2: <span class="math-tex">\(2\times 0.3+3\times x+4 \times y+5\times 0.2=3.4\)</span>, and thus <span class="math-tex">\(3x+4y=1.8\)</span></p><p>Solving these linear simultaneous equations on the GDC, we obtain <span class="math-tex">\(x=0.2\)</span> and <span class="math-tex">\(y=0.3\)</span>.</p></div><div class="remove-section" style="display: none;" title="Remove question field"> </div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="totals"><span class="score"></span><button class="btn btn-success btn-block text-center check-total"><i class="fa fa-check-square-o"></i> Check</button></div></div><hr> </section> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-default"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Exam Style Questions</p> </div> </div> <div class="panel-body"> <div> <p>The following questions are based on IB exam style questions from past exams. You should print these off (from the document at the top) and try to do these questions under exam conditions. Then you can check your work with the video solution.</p> <div class="panel panel-has-colored-body panel-default"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Question 1</p> </div> </div> <div class="panel-body"> <div> <p dir="ltr" id="docs-internal-guid-3f06b21f-7fff-c9c2-d0a9-a2feaacf8f52">Jenni plays a game using a spinner. The values on the spinner are labelled -5,0,3 and 10. The score for the game, X, is the value the spinner lands on. The following table shows the probability distribution for X.</p> <table align="center" border="2" cellpadding="1" cellspacing="1" style="width:100%;"> <tbody> <tr> <td>Score X</td> <td>-5</td> <td>0</td> <td>3</td> <td>10</td> </tr> <tr> <td>P(X=x)</td> <td>0.29</td> <td>a</td> <td>0.39</td> <td>0.19</td> </tr> </tbody> </table> <table align="left" dir="ltr" style="width:718px;"> <colgroup> <col> <col> <col> <col> <col> </colgroup> <tbody> <tr> <td> </td> </tr> </tbody> </table> <div style="clear:both;"> </div> <ol style="list-style-type:lower-alpha;"> <li dir="ltr"> <p dir="ltr" role="presentation">What is the value of a?</p> </li> </ol> <p dir="ltr" style="text-align: right;">(1)</p> <ol style="list-style-type:lower-alpha;"> <li dir="ltr" value="2"> <p dir="ltr" role="presentation">What is Jenni’s expected score if she plays the game once? </p> </li> </ol> <p dir="ltr" style="margin-left: 36pt; text-align: right;">(2)</p> <p dir="ltr" style="margin-left:36pt;">Jenni plays this game at a fair, and wins the amount in $ that the spinner lands on. </p> <ol style="list-style-type:lower-alpha;"> <li dir="ltr" value="3"> <p dir="ltr" role="presentation">What would be a fair price for Jenni to pay?</p> </li> </ol> <p dir="ltr" style="margin-left: 36pt; text-align: right;">(1)</p> <ol style="list-style-type:lower-alpha;"> <li dir="ltr" value="4"> <p dir="ltr" role="presentation">Jenni plays the game twice and adds up her scores. What is the probability that she gets a total score of 3? </p> </li> </ol> <p dir="ltr" style="margin-left: 108pt; text-align: right;">(3)</p> <p dir="ltr" style="margin-left: 108pt; text-align: right;">(7 marks)</p> <p dir="ltr" style="margin-left: 108pt;">Video solution </p> </div> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden"> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/598304701?badge=0&autopause=0&player_id=0&app_id=58479&h=e8173e4e6b"></iframe></div> <script src="../../../api/player.js"></script></section> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-default panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Question 2</p> </div> </div> <div class="panel-body"> <div> <p dir="ltr" id="docs-internal-guid-d93a3e9f-7fff-9457-5269-c9e80956776f">The following table shows the probability distribution of a discrete random variable A.</p> <table align="left" dir="ltr" style="width:718px;"> <colgroup> <col> <col> <col> <col> <col> </colgroup> <tbody> <tr> <td> <p dir="ltr">a</p> </td> <td> <p dir="ltr">2</p> </td> <td> <p dir="ltr">3</p> </td> <td> <p dir="ltr">4</p> </td> <td> <p dir="ltr">5</p> </td> </tr> <tr> <td> <p dir="ltr">P(A=a)</p> </td> <td> <p dir="ltr">0.3</p> </td> <td> <p dir="ltr">x</p> </td> <td> <p dir="ltr">y</p> </td> <td> <p dir="ltr">0.2</p> </td> </tr> </tbody> </table> <div style="clear:both;"> </div> <p dir="ltr">Given that E(A)=3.4, find the value of x and y. </p> <p dir="ltr">(4 marks)</p> </div> </div> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden"> 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