{"id":1545,"date":"2020-04-01T14:45:26","date_gmt":"2020-04-01T14:45:26","guid":{"rendered":"http:\/\/ibalmaths.com\/?post_type=knowledgebase&#038;p=1545"},"modified":"2020-04-02T10:34:33","modified_gmt":"2020-04-02T10:34:33","slug":"ibdp-past-year-exam-questions-discrete-random-variables","status":"publish","type":"knowledgebase","link":"https:\/\/ibalmaths.com\/index.php\/ibdp-math-hl-2\/discrete-random-variables\/ibdp-past-year-exam-questions-discrete-random-variables\/","title":{"rendered":"IBDP Past Year Exam Questions &#8211; Discrete Random Variables"},"content":{"rendered":"<p><strong>1. [M08\/P1\/TZ2]<\/strong><\/p>\r\n<p>The probability distribution of a discrete random variable <em>X<\/em> is defined by<\/p>\r\n<p>\r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>P<\/mi><mo>(<\/mo><mi>X<\/mi><mo>=<\/mo><mi>x<\/mi><mo>)<\/mo><mo>=<\/mo><mi>c<\/mi><mi>x<\/mi><mo>(<\/mo><mn>5<\/mn><mo>&#8211;<\/mo><mi>x<\/mi><mo>)<\/mo><mo>,<\/mo><mo>&#160;<\/mo><mo>&#160;<\/mo><mo>&#160;<\/mo><mo>&#160;<\/mo><mi>x<\/mi><mo>=<\/mo><mn>1<\/mn><mo>,<\/mo><mo>&#160;<\/mo><mn>2<\/mn><mo>,<\/mo><mo>&#160;<\/mo><mn>3<\/mn><mo>,<\/mo><mo>&#160;<\/mo><mn>4<\/mn><mo>.<\/mo><\/math>\r\n<\/p>\r\n<p>(a)\u00a0 \u00a0Find the value of \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>c<\/mi><\/math>\r\n .\u00a0 \u00a0[3 marks]<\/p>\r\n<p>(b)\u00a0 \u00a0Find\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>E<\/mi><mo>(<\/mo><mi>X<\/mi><mo>)<\/mo><\/math>\r\n .\u00a0 [3 marks]<\/p>\r\n<div id=\"link1-link-1545\" class=\"sh-link link1-link sh-hide\"><a href=\"#\" onclick=\"showhide_toggle('link1', 1545, 'Solution', 'Hide Solution'); return false;\" aria-expanded=\"false\"><span id=\"link1-toggle-1545\">Solution<\/span><\/a><\/div><div id=\"link1-content-1545\" class=\"sh-content link1-content sh-hide\" style=\"display: none;\"><\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1548\" src=\"http:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-10.jpg\" alt=\"\" width=\"878\" height=\"266\" srcset=\"https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-10.jpg 878w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-10-300x91.jpg 300w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-10-768x233.jpg 768w\" sizes=\"auto, (max-width: 878px) 100vw, 878px\" \/><\/p>\r\n<p>\u00a0<\/div>\r\n<p><strong>2. [M08\/P2\/TZ2]<\/strong><\/p>\r\n<p>Over a one month period, Ava and Sven play a total of <em>n<\/em> games of tennis. The probability that Ava wins any game is 0.4. The result of each game played is independent of any other game played.<br \/>\r\nLet X denote the number of games won by Ava over a one month period.<br \/>\r\n(a) Find an expression for P(X = 2) in terms of <em>n<\/em>.\u00a0 \u00a0[3 marks]<br \/>\r\n(b) If the probability that Ava wins two games is 0.121 correct to three<br \/>\r\ndecimal places, find the value of <em>n<\/em>.\u00a0 \u00a0[3 marks]<\/p>\r\n<div id=\"link2-link-1545\" class=\"sh-link link2-link sh-hide\"><a href=\"#\" onclick=\"showhide_toggle('link2', 1545, 'Solution', 'Hide Solution'); return false;\" aria-expanded=\"false\"><span id=\"link2-toggle-1545\">Solution<\/span><\/a><\/div><div id=\"link2-content-1545\" class=\"sh-content link2-content sh-hide\" style=\"display: none;\"><\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1550\" src=\"http:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-11.jpg\" alt=\"\" width=\"936\" height=\"350\" srcset=\"https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-11.jpg 936w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-11-300x112.jpg 300w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-11-768x287.jpg 768w\" sizes=\"auto, (max-width: 936px) 100vw, 936px\" \/><\/p>\r\n<p>\u00a0<\/div>\r\n<p><strong>3. [N08\/P1\/TZ0]<\/strong><\/p>\r\n<p>John removes the labels from three cans of tomato soup and two cans of chicken soup in order to enter a competition, and puts the cans away. He then discovers that the cans are identical, so that he cannot distinguish between cans of tomato soup and chicken soup. Some weeks later he decides to have a can of chicken soup for lunch.<br \/>\r\nHe opens the cans at random until he opens a can of chicken soup. Let Y denote the number of cans he opens. Find<br \/>\r\n(a) the possible values of Y ,\u00a0 \u00a0[1 mark]<br \/>\r\n(b) the probability of each of these values of Y ,\u00a0 \u00a0[4 marks]<br \/>\r\n(c) the expected value of Y .\u00a0 \u00a0[2 marks]<\/p>\r\n<div id=\"link3-link-1545\" class=\"sh-link link3-link sh-hide\"><a href=\"#\" onclick=\"showhide_toggle('link3', 1545, 'Solution', 'Hide Solution'); return false;\" aria-expanded=\"false\"><span id=\"link3-toggle-1545\">Solution<\/span><\/a><\/div><div id=\"link3-content-1545\" class=\"sh-content link3-content sh-hide\" style=\"display: none;\"><\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1551\" src=\"http:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-12.jpg\" alt=\"\" width=\"936\" height=\"458\" srcset=\"https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-12.jpg 936w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-12-300x147.jpg 300w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-12-768x376.jpg 768w\" sizes=\"auto, (max-width: 936px) 100vw, 936px\" \/><\/p>\r\n<p>\u00a0<\/div>\r\n<p><strong>4. [M99\/P1]<\/strong><\/p>\r\n<p>A biased die with four faces is used in a game. A player pays 10 counters to roll the die. The table below shows the possible scores on the die, the probability of each score and the number of counters the player receives in return for each score.<\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1554\" src=\"http:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-13.jpg\" alt=\"\" width=\"1037\" height=\"335\" srcset=\"https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-13.jpg 1037w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-13-300x97.jpg 300w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-13-1024x331.jpg 1024w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-13-768x248.jpg 768w\" sizes=\"auto, (max-width: 1037px) 100vw, 1037px\" \/><\/p>\r\n<p>Find the value of\u00a0 <em>n <\/em>in order for the player to get an expected return of 9 counters per poll.\u00a0 \u00a0[4 marks]<\/p>\r\n<div id=\"link4-link-1545\" class=\"sh-link link4-link sh-hide\"><a href=\"#\" onclick=\"showhide_toggle('link4', 1545, 'Solution', 'Hide Solution'); return false;\" aria-expanded=\"false\"><span id=\"link4-toggle-1545\">Solution<\/span><\/a><\/div><div id=\"link4-content-1545\" class=\"sh-content link4-content sh-hide\" style=\"display: none;\"><\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1555\" src=\"http:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-14.jpg\" alt=\"\" width=\"1288\" height=\"447\" srcset=\"https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-14.jpg 1288w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-14-300x104.jpg 300w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-14-1024x355.jpg 1024w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-14-768x267.jpg 768w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-14-1200x416.jpg 1200w\" sizes=\"auto, (max-width: 1288px) 100vw, 1288px\" \/><\/p>\r\n<p>\u00a0<\/div>\r\n<p><strong>5. [M10\/P1\/TZ2]<\/strong><\/p>\r\n<p>A biased coin is weighted such that the probability of obtaining a head is\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfrac><mn>4<\/mn><mn>7<\/mn><\/mfrac><\/math>\r\n . The coin is tossed 6 times and <em>X<\/em> denotes the number of heads observed. Find the value of the ratio\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfrac><mrow><mi>P<\/mi><mfenced><mrow><mi>X<\/mi><mo>=<\/mo><mn>3<\/mn><\/mrow><\/mfenced><\/mrow><mrow><mi>P<\/mi><mfenced><mrow><mi>X<\/mi><mo>=<\/mo><mn>2<\/mn><\/mrow><\/mfenced><\/mrow><\/mfrac><\/math>\r\n .<\/p>\r\n<div id=\"link5-link-1545\" class=\"sh-link link5-link sh-hide\"><a href=\"#\" onclick=\"showhide_toggle('link5', 1545, 'Solution', 'Hide Solution'); return false;\" aria-expanded=\"false\"><span id=\"link5-toggle-1545\">Solution<\/span><\/a><\/div><div id=\"link5-content-1545\" class=\"sh-content link5-content sh-hide\" style=\"display: none;\"><\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1564\" src=\"http:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-15.jpg\" alt=\"\" width=\"936\" height=\"320\" srcset=\"https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-15.jpg 936w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-15-300x103.jpg 300w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-15-768x263.jpg 768w\" sizes=\"auto, (max-width: 936px) 100vw, 936px\" \/><\/p>\r\n<p>\u00a0<\/div>\r\n<p><strong>6. [M13\/P1\/TZ1]<\/strong><\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1566\" src=\"http:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-16.jpg\" alt=\"\" width=\"1184\" height=\"1525\" srcset=\"https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-16.jpg 1184w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-16-233x300.jpg 233w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-16-795x1024.jpg 795w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-16-768x989.jpg 768w\" sizes=\"auto, (max-width: 1184px) 100vw, 1184px\" \/><\/p>\r\n<div id=\"link6-link-1545\" class=\"sh-link link6-link sh-hide\"><a href=\"#\" onclick=\"showhide_toggle('link6', 1545, 'Solution', 'Hide Solution'); return false;\" aria-expanded=\"false\"><span id=\"link6-toggle-1545\">Solution<\/span><\/a><\/div><div id=\"link6-content-1545\" class=\"sh-content link6-content sh-hide\" style=\"display: none;\"><\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1567\" src=\"http:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-17.jpg\" alt=\"\" width=\"936\" height=\"2473\" srcset=\"https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-17.jpg 936w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-17-114x300.jpg 114w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-17-388x1024.jpg 388w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-17-768x2029.jpg 768w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-17-581x1536.jpg 581w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-17-775x2048.jpg 775w\" sizes=\"auto, (max-width: 936px) 100vw, 936px\" \/><\/p>\r\n<p>\u00a0<\/div>\r\n<p><strong>7. [N13\/P1\/TZ0]<\/strong><\/p>\r\n<p>The discrete random variable <em>X<\/em> has probability distribution:<\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1569\" src=\"http:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-18.jpg\" alt=\"\" width=\"655\" height=\"133\" srcset=\"https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-18.jpg 655w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-18-300x61.jpg 300w\" sizes=\"auto, (max-width: 655px) 100vw, 655px\" \/><\/p>\r\n<p>(a) Find the value of <em>a<\/em> .\u00a0 \u00a0 [1]<br \/>\r\n(b) Find E(<em>X<\/em> ) .\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0[2]<br \/>\r\n(c) Find Var (<em>X<\/em> ) .\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 [3]<\/p>\r\n<div id=\"link7-link-1545\" class=\"sh-link link7-link sh-hide\"><a href=\"#\" onclick=\"showhide_toggle('link7', 1545, 'Solution', 'Hide Solution'); return false;\" aria-expanded=\"false\"><span id=\"link7-toggle-1545\">Solution<\/span><\/a><\/div><div id=\"link7-content-1545\" class=\"sh-content link7-content sh-hide\" style=\"display: none;\"><\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1570\" src=\"http:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-19.jpg\" alt=\"\" width=\"966\" height=\"624\" srcset=\"https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-19.jpg 966w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-19-300x194.jpg 300w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-19-768x496.jpg 768w\" sizes=\"auto, (max-width: 966px) 100vw, 966px\" \/><\/p>\r\n<p>\u00a0<\/div>\r\n<p><strong>8. [M16\/P1\/TZ2]<\/strong><\/p>\r\n<p>A biased coin is tossed five times. The probability of obtaining a head in any one throw is <em>p<\/em> .<br \/>\r\nLet X be the number of heads obtained.<\/p>\r\n<p>(a) Find, in terms of\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>p<\/mi><\/math>\r\n , an expression for P(X = 4) .\u00a0 \u00a0[2 marks]<\/p>\r\n<p>(b)\u00a0 \u00a0 (i) Determine the value of\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>p<\/mi><\/math>\r\n for which P(X = 4) is a maximum.<br \/>\r\n\u00a0 \u00a0 \u00a0 \u00a0 (ii) For this value of <em> \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>p<\/mi><\/math>\r\n <\/em> , determine the expected number of heads. [6 marks]<\/p>\r\n<div id=\"link8-link-1545\" class=\"sh-link link8-link sh-hide\"><a href=\"#\" onclick=\"showhide_toggle('link8', 1545, 'Solution', 'Hide Solution'); return false;\" aria-expanded=\"false\"><span id=\"link8-toggle-1545\">Solution<\/span><\/a><\/div><div id=\"link8-content-1545\" class=\"sh-content link8-content sh-hide\" style=\"display: none;\"><\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1577\" src=\"http:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-20.jpg\" alt=\"\" width=\"986\" height=\"516\" srcset=\"https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-20.jpg 986w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-20-300x157.jpg 300w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-20-768x402.jpg 768w\" sizes=\"auto, (max-width: 986px) 100vw, 986px\" \/><\/p>\r\n<p>\u00a0<\/div>\r\n<p><strong>9. [N17\/P1\/TZ0]<\/strong><\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1581\" src=\"http:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-21.jpg\" alt=\"\" width=\"1125\" height=\"914\" srcset=\"https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-21.jpg 1125w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-21-300x244.jpg 300w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-21-1024x832.jpg 1024w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-21-768x624.jpg 768w\" sizes=\"auto, (max-width: 1125px) 100vw, 1125px\" \/><\/p>\r\n<div id=\"link9-link-1545\" class=\"sh-link link9-link sh-hide\"><a href=\"#\" onclick=\"showhide_toggle('link9', 1545, 'Solution', 'Hide Solution'); return false;\" aria-expanded=\"false\"><span id=\"link9-toggle-1545\">Solution<\/span><\/a><\/div><div id=\"link9-content-1545\" class=\"sh-content link9-content sh-hide\" style=\"display: none;\"><\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1583\" src=\"http:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-22.jpg\" alt=\"\" width=\"1125\" height=\"914\" srcset=\"https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-22.jpg 1125w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-22-300x244.jpg 300w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-22-1024x832.jpg 1024w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-22-768x624.jpg 768w\" sizes=\"auto, (max-width: 1125px) 100vw, 1125px\" \/><\/p>\r\n<p>\u00a0<\/div>\r\n<p><strong>10. [M14\/P1\/TZ2]<\/strong><\/p>\r\n<p>In a pack of seven transistors, three are found to be defective. Three transistors are selected from the pack at random without replacement. The discrete random variable X represents the number of defective transistors selected.<\/p>\r\n<p>(i) Find\u00a0\r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>P<\/mi><mfenced><mrow><mi>X<\/mi><mo>=<\/mo><mn>2<\/mn><\/mrow><\/mfenced><\/math>\r\n .<br \/>\r\n(ii) <strong>Copy<\/strong> and complete the following table:<\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1585\" src=\"http:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-23.jpg\" alt=\"\" width=\"657\" height=\"105\" srcset=\"https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-23.jpg 657w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-23-300x48.jpg 300w\" sizes=\"auto, (max-width: 657px) 100vw, 657px\" \/><\/p>\r\n<p>(iii) Determine\u00a0\r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>E<\/mi><mfenced><mi>X<\/mi><\/mfenced><\/math>\r\n .\u00a0 \u00a0 [6]<\/p>\r\n<div id=\"link10-link-1545\" class=\"sh-link link10-link sh-hide\"><a href=\"#\" onclick=\"showhide_toggle('link10', 1545, 'Solution', 'Hide Solution'); return false;\" aria-expanded=\"false\"><span id=\"link10-toggle-1545\">Solution<\/span><\/a><\/div><div id=\"link10-content-1545\" class=\"sh-content link10-content sh-hide\" style=\"display: none;\"><\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1586\" src=\"http:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-24.jpg\" alt=\"\" width=\"890\" height=\"951\" srcset=\"https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-24.jpg 890w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-24-281x300.jpg 281w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-24-768x821.jpg 768w\" sizes=\"auto, (max-width: 890px) 100vw, 890px\" \/><\/p>\r\n<p>\u00a0<\/div>\r\n<p>&nbsp;<\/p><!-- AddThis Advanced Settings generic via filter on the_content --><!-- AddThis Share Buttons generic via filter on the_content -->","protected":false},"excerpt":{"rendered":"1. [M08\/P1\/TZ2] The probability distribution of a discrete random variable X is defined by P(X=x)=cx(5&#8211;x),&#160;&#160;&#160;&#160;x=1,&#160;2,&#160;3,&#160;4. (a)\u00a0 \u00a0Find the value of c .\u00a0 \u00a0[3 marks] (b)\u00a0 \u00a0Find\u00a0 E(X) .\u00a0 [3 marks] 2. [M08\/P2\/TZ2] Over a one month period, Ava and Sven play a total of n games of tennis. The probability that Ava wins any game [&hellip;]<!-- AddThis Advanced Settings generic via filter on get_the_excerpt --><!-- AddThis Share Buttons generic via filter on get_the_excerpt -->","protected":false},"author":4,"featured_media":0,"comment_status":"closed","ping_status":"closed","template":"","class_list":["post-1545","knowledgebase","type-knowledgebase","status-publish","hentry","knowledgebase_cat-discrete-random-variables","no-wpautop"],"_links":{"self":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase\/1545","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase"}],"about":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/types\/knowledgebase"}],"author":[{"embeddable":true,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/comments?post=1545"}],"version-history":[{"count":17,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase\/1545\/revisions"}],"predecessor-version":[{"id":1588,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase\/1545\/revisions\/1588"}],"wp:attachment":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/media?parent=1545"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}