{"id":242,"date":"2021-07-14T15:58:57","date_gmt":"2021-07-14T15:58:57","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/chapter\/probability-distribution-function-pdf-for-a-discrete-random-variable\/"},"modified":"2023-12-05T09:07:33","modified_gmt":"2023-12-05T09:07:33","slug":"probability-distribution-function-pdf-for-a-discrete-random-variable","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/chapter\/probability-distribution-function-pdf-for-a-discrete-random-variable\/","title":{"raw":"What is a Probability Distribution Function?","rendered":"What is a Probability Distribution Function?"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Describe the two characteristics of a probability distribution for a discrete random variable<\/li>\r\n \t<li>Create a discrete probability distribution for a given discrete random variable<\/li>\r\n<\/ul>\r\n<\/div>\r\nThe idea of a random variable can be confusing. In this video we help you learn what a random variable is, and the difference between discrete and continuous random variables.\r\n\r\nhttps:\/\/www.youtube.com\/embed\/lHCpYeFvTs0\r\n\r\nA discrete <span data-type=\"term\">probability distribution function<\/span> has two characteristics:\r\n<ol id=\"element-yu2\" data-number-style=\"arabic\">\r\n \t<li>Each probability is between zero and one, inclusive.<\/li>\r\n \t<li>The sum of the probabilities is one.<\/li>\r\n<\/ol>\r\n<div id=\"example1\" class=\"example\" data-type=\"example\"><section>\r\n<div class=\"textbox exercises\">\r\n<h3 id=\"element-165\">Example<\/h3>\r\nA child psychologist is interested in the number of times a newborn baby's crying wakes its mother after midnight. For a random sample of 50 mothers, the following information was obtained. Let [latex]X=[\/latex] the number of times per week a newborn baby's crying wakes its mother after midnight. For this example, [latex]x = 0, 1, 2, 3, 4, 5[\/latex].\r\n<p id=\"fs-idp70402976\">[latex]P(x) =[\/latex]<span style=\"font-size: 1rem; text-align: initial;\">\u00a0probability that [latex]X[\/latex]<\/span><span style=\"font-size: 1rem; text-align: initial;\">\u00a0takes on a value <\/span>[latex]x[\/latex]<span style=\"font-size: 1rem; text-align: initial;\">.<\/span><\/p>\r\n\r\n<table id=\"M02_Ch04_tbl001\" style=\"height: 77px;\" summary=\"PDF table for the the number of times a newborn wakes its mother after midnight and probabilities.\">\r\n<thead>\r\n<tr style=\"height: 11px;\">\r\n<th style=\"height: 11px; width: 135.656px;\">[latex]x[\/latex]<\/th>\r\n<th style=\"height: 11px; width: 194.656px;\">[latex]P(x)[\/latex]<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr style=\"height: 11px;\">\r\n<td style=\"height: 11px; width: 135.656px;\">[latex]0[\/latex]<\/td>\r\n<td style=\"height: 11px; width: 194.656px;\">[latex]P(x = 0)[\/latex] [latex]=[\/latex] [latex](\\frac{2}{50})[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 11px;\">\r\n<td style=\"height: 11px; width: 135.656px;\">[latex]1[\/latex]<\/td>\r\n<td style=\"height: 11px; width: 194.656px;\">[latex]P(x = 1)[\/latex] [latex]=[\/latex]\u00a0[latex](\\frac{11}{50})[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 11px;\">\r\n<td style=\"height: 11px; width: 135.656px;\">[latex]2[\/latex]<\/td>\r\n<td style=\"height: 11px; width: 194.656px;\">[latex]P(x = 2) =[\/latex]\u00a0[latex](\\frac{23}{50})[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 11px;\">\r\n<td style=\"height: 11px; width: 135.656px;\">[latex]3[\/latex]<\/td>\r\n<td style=\"height: 11px; width: 194.656px;\">[latex]P(x = 3) =[\/latex]\u00a0[latex](\\frac{9}{50)}[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 11px;\">\r\n<td style=\"height: 11px; width: 135.656px;\">[latex]4[\/latex]<\/td>\r\n<td style=\"height: 11px; width: 194.656px;\">[latex]P(x = 4) =[\/latex]\u00a0[latex](\\frac{4}{50})[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 11px;\">\r\n<td style=\"height: 11px; width: 135.656px;\">[latex]5[\/latex]<\/td>\r\n<td style=\"height: 11px; width: 194.656px;\">[latex]P(x = 5) =[\/latex]\u00a0[latex](\\frac{1}{50})[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p id=\"element-260\">[latex]X[\/latex] takes on the values [latex]0, 1, 2, 3, 4, 5.[\/latex] This is a discrete PDF because:<\/p>\r\n\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li>Each [latex]P(x)[\/latex] is between zero and one, inclusive.<\/li>\r\n \t<li>The sum of the probabilities is one, that is,<\/li>\r\n<\/ol>\r\n<div id=\"fifsum\" class=\"equation\" data-type=\"equation\">\r\n<div style=\"text-align: center;\">[latex](\\frac{2}{50})+(\\frac{11}{50})+(\\frac{23}{50})+(\\frac{9}{50})+(\\frac{4}{50})+(\\frac{1}{50})=1[\/latex]<\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"element-852\" class=\"example\" data-type=\"example\"><section>\r\n<div class=\"textbox key-takeaways\">\r\n<h3 id=\"element-500\">Try it<\/h3>\r\nA hospital researcher is interested in the number of times the average post-op patient will ring the nurse during a 12-hour shift. For a random sample of 50 patients, the following information was obtained. Let [latex]X=[\/latex]\u00a0the number of times a patient rings the nurse during a 12-hour shift. For this exercise, [latex]X=0, 1, 2, 3, 4, 5[\/latex]. [latex]P(x)[\/latex] = the probability that [latex]X[\/latex]\u00a0takes on value [latex]x[\/latex]. Why is this a discrete probability distribution function (two reasons)?\r\n<table summary=\"Table 4.3 \" data-id=\"fs-idp71433824\">\r\n<thead>\r\n<tr>\r\n<th scope=\"col\">[latex]X[\/latex]<\/th>\r\n<th scope=\"col\">[latex]P(x)[\/latex]<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr>\r\n<td>[latex]0[\/latex]<\/td>\r\n<td>[latex]P(x= 0) = \\frac{4}{50}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]1[\/latex]<\/td>\r\n<td>[latex]P(x= 1) = \\frac{8}{50}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]2[\/latex]<\/td>\r\n<td>[latex]P(x= 2) = \\frac{16}{50}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]3[\/latex]<\/td>\r\n<td>[latex]P(x= 3) = \\frac{14}{50}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]4[\/latex]<\/td>\r\n<td>[latex]P(x= 4) = \\frac{6}{50}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]5[\/latex]<\/td>\r\n<td>[latex]P(x= 5) = \\frac{2}{50}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<div id=\"eip-694\" class=\"exercise\" data-type=\"exercise\"><section>\r\n<div><\/div>\r\n<\/section><\/div>\r\n<\/div>\r\n<\/section>\r\n<div><\/div>\r\n<\/div>\r\n<\/section><\/div>\r\n<div id=\"fs-idm96796576\" class=\"note statistics try ui-has-child-title\" data-type=\"note\" data-has-label=\"true\" data-label=\"\">\r\n<div id=\"element-852\" class=\"example\" data-type=\"example\"><section>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nSuppose Nancy has classes three days a week. She attends classes three days a week\u00a0[latex]80[\/latex]% of the time, two days [latex]15[\/latex]%\u00a0of the time, one day [latex]4[\/latex]%\u00a0of the time, and no days [latex]1[\/latex]%\u00a0<span style=\"font-size: 1rem; text-align: initial;\">of the time. Suppose one week is randomly selected.<\/span>\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li data-type=\"newline\" data-count=\"2\">Let [latex]X[\/latex] = the number of days Nancy ____________________.<\/li>\r\n \t<li id=\"eip-466\" class=\"exercise\" data-type=\"exercise\"><section>\r\n<div id=\"eip-idp214323360\" class=\"solution ui-solution-visible\" data-type=\"solution\">\r\n<div class=\"ui-toggle-wrapper\">[latex]X[\/latex] takes on what values?<\/div>\r\n<\/div>\r\n<\/section><\/li>\r\n \t<li id=\"eip-694\" class=\"exercise\" data-type=\"exercise\"><section>\r\n<div id=\"eip-idm30850864\" class=\"solution ui-solution-visible\" data-type=\"solution\">\r\n<div class=\"ui-toggle-wrapper\">Suppose one week is randomly chosen. Construct a probability distribution table (called a PDF table) like the one in the previous Try It. The table should have two columns labeled [latex]x[\/latex] and [latex]P(x)[\/latex]. What does the [latex]P(x)[\/latex] column sum to?<\/div>\r\n<\/div>\r\n<\/section>\r\n<div><\/div><\/li>\r\n<\/ol>\r\n[reveal-answer q=\"139967\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"139967\"]\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li>Let [latex]X=[\/latex] the number of days Nancy attends class per week.<\/li>\r\n \t<li>[latex]0,1,2, \\ \\mathrm{and}\\ 3[\/latex]<\/li>\r\n \t<li>\r\n<table summary=\"Table 4.4 \" data-id=\"eip-idp64719200\">\r\n<thead>\r\n<tr>\r\n<th scope=\"col\">[latex]x[\/latex]<\/th>\r\n<th scope=\"col\">[latex]P(x)[\/latex]<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr>\r\n<td>[latex]0[\/latex]<\/td>\r\n<td>[latex]0.01[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]1[\/latex]<\/td>\r\n<td>[latex]0.04[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]2[\/latex]<\/td>\r\n<td>[latex]0.15[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]3[\/latex]<\/td>\r\n<td>[latex]0.80[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/li>\r\n<\/ol>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div id=\"example1\" class=\"example\" data-type=\"example\"><section>\r\n<div id=\"element-852\" class=\"example\" data-type=\"example\"><section>\r\n<div class=\"textbox key-takeaways\">\r\n<h3 id=\"element-500\">Try it<\/h3>\r\n<div id=\"fs-idm96796576\" class=\"note statistics try ui-has-child-title\" data-type=\"note\" data-has-label=\"true\" data-label=\"\">\r\n<div id=\"fs-idm157100592\" class=\"note statistics try ui-has-child-title\" data-type=\"note\" data-has-label=\"true\" data-label=\"\"><section>\r\n<div id=\"fs-idp17767152\" class=\"exercise\" data-type=\"exercise\"><section>\r\n<div id=\"fs-idm59642592\" class=\"problem\" data-type=\"problem\">\r\n<p id=\"fs-idp10711280\">Jeremiah has basketball practice two days a week. Ninety percent of the time, he attends both practices. Eight percent of the time, he attends one practice. Two percent of the time, he does not attend either practice. What is\u00a0[latex]X[\/latex]\u00a0and what values does it take on?<\/p>\r\n[reveal-answer q=\"716822\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"716822\"]\r\n\r\n[latex]X[\/latex] is the number of days Jeremiah attends basketball practice per week. [latex]X[\/latex] takes on the values [latex]0, 1,[\/latex] and [latex]2.[\/latex]\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n<\/section><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/section><\/div>\r\n<\/section><\/div>\r\n<\/section><\/div>\r\n<div id=\"fs-idm157100592\" class=\"note statistics try ui-has-child-title\" data-type=\"note\" data-has-label=\"true\" data-label=\"\"><\/div>\r\n<\/div>\r\n<div class=\"note statistics try ui-has-child-title\" data-type=\"note\" data-has-label=\"true\" data-label=\"\"><\/div>","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Describe the two characteristics of a probability distribution for a discrete random variable<\/li>\n<li>Create a discrete probability distribution for a given discrete random variable<\/li>\n<\/ul>\n<\/div>\n<p>The idea of a random variable can be confusing. In this video we help you learn what a random variable is, and the difference between discrete and continuous random variables.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Random Variables and Probability Distributions\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/lHCpYeFvTs0?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>A discrete <span data-type=\"term\">probability distribution function<\/span> has two characteristics:<\/p>\n<ol id=\"element-yu2\" data-number-style=\"arabic\">\n<li>Each probability is between zero and one, inclusive.<\/li>\n<li>The sum of the probabilities is one.<\/li>\n<\/ol>\n<div id=\"example1\" class=\"example\" data-type=\"example\">\n<section>\n<div class=\"textbox exercises\">\n<h3 id=\"element-165\">Example<\/h3>\n<p>A child psychologist is interested in the number of times a newborn baby&#8217;s crying wakes its mother after midnight. For a random sample of 50 mothers, the following information was obtained. Let [latex]X=[\/latex] the number of times per week a newborn baby&#8217;s crying wakes its mother after midnight. For this example, [latex]x = 0, 1, 2, 3, 4, 5[\/latex].<\/p>\n<p id=\"fs-idp70402976\">[latex]P(x) =[\/latex]<span style=\"font-size: 1rem; text-align: initial;\">\u00a0probability that [latex]X[\/latex]<\/span><span style=\"font-size: 1rem; text-align: initial;\">\u00a0takes on a value <\/span>[latex]x[\/latex]<span style=\"font-size: 1rem; text-align: initial;\">.<\/span><\/p>\n<table id=\"M02_Ch04_tbl001\" style=\"height: 77px;\" summary=\"PDF table for the the number of times a newborn wakes its mother after midnight and probabilities.\">\n<thead>\n<tr style=\"height: 11px;\">\n<th style=\"height: 11px; width: 135.656px;\">[latex]x[\/latex]<\/th>\n<th style=\"height: 11px; width: 194.656px;\">[latex]P(x)[\/latex]<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr style=\"height: 11px;\">\n<td style=\"height: 11px; width: 135.656px;\">[latex]0[\/latex]<\/td>\n<td style=\"height: 11px; width: 194.656px;\">[latex]P(x = 0)[\/latex] [latex]=[\/latex] [latex](\\frac{2}{50})[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 11px;\">\n<td style=\"height: 11px; width: 135.656px;\">[latex]1[\/latex]<\/td>\n<td style=\"height: 11px; width: 194.656px;\">[latex]P(x = 1)[\/latex] [latex]=[\/latex]\u00a0[latex](\\frac{11}{50})[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 11px;\">\n<td style=\"height: 11px; width: 135.656px;\">[latex]2[\/latex]<\/td>\n<td style=\"height: 11px; width: 194.656px;\">[latex]P(x = 2) =[\/latex]\u00a0[latex](\\frac{23}{50})[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 11px;\">\n<td style=\"height: 11px; width: 135.656px;\">[latex]3[\/latex]<\/td>\n<td style=\"height: 11px; width: 194.656px;\">[latex]P(x = 3) =[\/latex]\u00a0[latex](\\frac{9}{50)}[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 11px;\">\n<td style=\"height: 11px; width: 135.656px;\">[latex]4[\/latex]<\/td>\n<td style=\"height: 11px; width: 194.656px;\">[latex]P(x = 4) =[\/latex]\u00a0[latex](\\frac{4}{50})[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 11px;\">\n<td style=\"height: 11px; width: 135.656px;\">[latex]5[\/latex]<\/td>\n<td style=\"height: 11px; width: 194.656px;\">[latex]P(x = 5) =[\/latex]\u00a0[latex](\\frac{1}{50})[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"element-260\">[latex]X[\/latex] takes on the values [latex]0, 1, 2, 3, 4, 5.[\/latex] This is a discrete PDF because:<\/p>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>Each [latex]P(x)[\/latex] is between zero and one, inclusive.<\/li>\n<li>The sum of the probabilities is one, that is,<\/li>\n<\/ol>\n<div id=\"fifsum\" class=\"equation\" data-type=\"equation\">\n<div style=\"text-align: center;\">[latex](\\frac{2}{50})+(\\frac{11}{50})+(\\frac{23}{50})+(\\frac{9}{50})+(\\frac{4}{50})+(\\frac{1}{50})=1[\/latex]<\/div>\n<\/div>\n<\/div>\n<div id=\"element-852\" class=\"example\" data-type=\"example\">\n<section>\n<div class=\"textbox key-takeaways\">\n<h3 id=\"element-500\">Try it<\/h3>\n<p>A hospital researcher is interested in the number of times the average post-op patient will ring the nurse during a 12-hour shift. For a random sample of 50 patients, the following information was obtained. Let [latex]X=[\/latex]\u00a0the number of times a patient rings the nurse during a 12-hour shift. For this exercise, [latex]X=0, 1, 2, 3, 4, 5[\/latex]. [latex]P(x)[\/latex] = the probability that [latex]X[\/latex]\u00a0takes on value [latex]x[\/latex]. Why is this a discrete probability distribution function (two reasons)?<\/p>\n<table summary=\"Table 4.3\" data-id=\"fs-idp71433824\">\n<thead>\n<tr>\n<th scope=\"col\">[latex]X[\/latex]<\/th>\n<th scope=\"col\">[latex]P(x)[\/latex]<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>[latex]0[\/latex]<\/td>\n<td>[latex]P(x= 0) = \\frac{4}{50}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]1[\/latex]<\/td>\n<td>[latex]P(x= 1) = \\frac{8}{50}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]2[\/latex]<\/td>\n<td>[latex]P(x= 2) = \\frac{16}{50}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]3[\/latex]<\/td>\n<td>[latex]P(x= 3) = \\frac{14}{50}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]4[\/latex]<\/td>\n<td>[latex]P(x= 4) = \\frac{6}{50}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]5[\/latex]<\/td>\n<td>[latex]P(x= 5) = \\frac{2}{50}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div id=\"eip-694\" class=\"exercise\" data-type=\"exercise\">\n<section>\n<div><\/div>\n<\/section>\n<\/div>\n<\/div>\n<\/section>\n<div><\/div>\n<\/div>\n<\/section>\n<\/div>\n<div id=\"fs-idm96796576\" class=\"note statistics try ui-has-child-title\" data-type=\"note\" data-has-label=\"true\" data-label=\"\">\n<div id=\"element-852\" class=\"example\" data-type=\"example\">\n<section>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Suppose Nancy has classes three days a week. She attends classes three days a week\u00a0[latex]80[\/latex]% of the time, two days [latex]15[\/latex]%\u00a0of the time, one day [latex]4[\/latex]%\u00a0of the time, and no days [latex]1[\/latex]%\u00a0<span style=\"font-size: 1rem; text-align: initial;\">of the time. Suppose one week is randomly selected.<\/span><\/p>\n<ol style=\"list-style-type: lower-alpha;\">\n<li data-type=\"newline\" data-count=\"2\">Let [latex]X[\/latex] = the number of days Nancy ____________________.<\/li>\n<li id=\"eip-466\" class=\"exercise\" data-type=\"exercise\">\n<section>\n<div id=\"eip-idp214323360\" class=\"solution ui-solution-visible\" data-type=\"solution\">\n<div class=\"ui-toggle-wrapper\">[latex]X[\/latex] takes on what values?<\/div>\n<\/div>\n<\/section>\n<\/li>\n<li id=\"eip-694\" class=\"exercise\" data-type=\"exercise\">\n<section>\n<div id=\"eip-idm30850864\" class=\"solution ui-solution-visible\" data-type=\"solution\">\n<div class=\"ui-toggle-wrapper\">Suppose one week is randomly chosen. Construct a probability distribution table (called a PDF table) like the one in the previous Try It. The table should have two columns labeled [latex]x[\/latex] and [latex]P(x)[\/latex]. What does the [latex]P(x)[\/latex] column sum to?<\/div>\n<\/div>\n<\/section>\n<div><\/div>\n<\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q139967\">Show Answer<\/span><\/p>\n<div id=\"q139967\" class=\"hidden-answer\" style=\"display: none\">\n<ol style=\"list-style-type: lower-alpha;\">\n<li>Let [latex]X=[\/latex] the number of days Nancy attends class per week.<\/li>\n<li>[latex]0,1,2, \\ \\mathrm{and}\\ 3[\/latex]<\/li>\n<li>\n<table summary=\"Table 4.4\" data-id=\"eip-idp64719200\">\n<thead>\n<tr>\n<th scope=\"col\">[latex]x[\/latex]<\/th>\n<th scope=\"col\">[latex]P(x)[\/latex]<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>[latex]0[\/latex]<\/td>\n<td>[latex]0.01[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]1[\/latex]<\/td>\n<td>[latex]0.04[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]2[\/latex]<\/td>\n<td>[latex]0.15[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]3[\/latex]<\/td>\n<td>[latex]0.80[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"example1\" class=\"example\" data-type=\"example\">\n<section>\n<div id=\"element-852\" class=\"example\" data-type=\"example\">\n<section>\n<div class=\"textbox key-takeaways\">\n<h3 id=\"element-500\">Try it<\/h3>\n<div id=\"fs-idm96796576\" class=\"note statistics try ui-has-child-title\" data-type=\"note\" data-has-label=\"true\" data-label=\"\">\n<div id=\"fs-idm157100592\" class=\"note statistics try ui-has-child-title\" data-type=\"note\" data-has-label=\"true\" data-label=\"\">\n<section>\n<div id=\"fs-idp17767152\" class=\"exercise\" data-type=\"exercise\">\n<section>\n<div id=\"fs-idm59642592\" class=\"problem\" data-type=\"problem\">\n<p id=\"fs-idp10711280\">Jeremiah has basketball practice two days a week. Ninety percent of the time, he attends both practices. Eight percent of the time, he attends one practice. Two percent of the time, he does not attend either practice. What is\u00a0[latex]X[\/latex]\u00a0and what values does it take on?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q716822\">Show Answer<\/span><\/p>\n<div id=\"q716822\" class=\"hidden-answer\" style=\"display: none\">\n<p>[latex]X[\/latex] is the number of days Jeremiah attends basketball practice per week. [latex]X[\/latex] takes on the values [latex]0, 1,[\/latex] and [latex]2.[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<\/div>\n<\/section>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<\/div>\n<\/section>\n<\/div>\n<\/section>\n<\/div>\n<div id=\"fs-idm157100592\" class=\"note statistics try ui-has-child-title\" data-type=\"note\" data-has-label=\"true\" data-label=\"\"><\/div>\n<\/div>\n<div class=\"note statistics try ui-has-child-title\" data-type=\"note\" data-has-label=\"true\" data-label=\"\"><\/div>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-242\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Introductory Statistics. <strong>Authored by<\/strong>: Barbara Illowsky, Susan Dean. <strong>Provided by<\/strong>: Open Stax. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/openstax.org\/books\/introductory-statistics\/pages\/1-introduction\">https:\/\/openstax.org\/books\/introductory-statistics\/pages\/1-introduction<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: Access for free at https:\/\/openstax.org\/books\/introductory-statistics\/pages\/1-introduction<\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">All rights reserved content<\/div><ul class=\"citation-list\"><li>Understanding Random Variables - Probability Distributions 1. <strong>Authored by<\/strong>: Statistics Learning Centre. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/www.youtube.com\/embed\/lHCpYeFvTs0\">https:\/\/www.youtube.com\/embed\/lHCpYeFvTs0<\/a>. <strong>License<\/strong>: <em>All Rights Reserved<\/em>. <strong>License Terms<\/strong>: Standard YouTube License<\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":169134,"menu_order":8,"template":"","meta":{"_candela_citation":"[{\"type\":\"copyrighted_video\",\"description\":\"Understanding Random Variables - Probability Distributions 1\",\"author\":\"Statistics Learning Centre\",\"organization\":\"\",\"url\":\"https:\/\/www.youtube.com\/embed\/lHCpYeFvTs0\",\"project\":\"\",\"license\":\"arr\",\"license_terms\":\"Standard YouTube License\"},{\"type\":\"cc\",\"description\":\"Introductory Statistics\",\"author\":\"Barbara Illowsky, Susan Dean\",\"organization\":\"Open Stax\",\"url\":\"https:\/\/openstax.org\/books\/introductory-statistics\/pages\/1-introduction\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Access for free at https:\/\/openstax.org\/books\/introductory-statistics\/pages\/1-introduction\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-242","chapter","type-chapter","status-publish","hentry"],"part":240,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/242","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/users\/169134"}],"version-history":[{"count":10,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/242\/revisions"}],"predecessor-version":[{"id":3504,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/242\/revisions\/3504"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/parts\/240"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/242\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/media?parent=242"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapter-type?post=242"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/contributor?post=242"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/license?post=242"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}