{"id":148,"date":"2016-04-21T22:43:44","date_gmt":"2016-04-21T22:43:44","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/introstats1xmaster\/?post_type=chapter&#038;p=148"},"modified":"2021-06-24T20:17:04","modified_gmt":"2021-06-24T20:17:04","slug":"probability-distribution-function-pdf-for-a-discrete-random-variable","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/ntcc-introstats1\/chapter\/probability-distribution-function-pdf-for-a-discrete-random-variable\/","title":{"raw":"4.1: Probability Distribution Function (PDF) for a Discrete Random Variable","rendered":"4.1: Probability Distribution Function (PDF) for a Discrete Random Variable"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Recognize and understand discrete probability distribution functions, in general<\/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 id=\"enumprac\" data-number-style=\"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>[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&nbsp;\r\n\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 key-takeaways\">\r\n<h3 id=\"element-500\">Try it<\/h3>\r\nSuppose Nancy has classes <strong>three days<\/strong> a week. She attends classes three days a week\u00a0<strong>[latex]80[\/latex]%<\/strong> of the time, <strong>two days <\/strong><strong>[latex]15[\/latex]%<\/strong>\u00a0of the time, <strong>one day [latex]4[\/latex]%<\/strong>\u00a0of the time, and <strong>no days [latex]1[\/latex]<\/strong><strong style=\"font-size: 1rem; text-align: initial;\">%\u00a0<\/strong><span style=\"font-size: 1rem; text-align: initial;\">of the time. Suppose one week is randomly selected.<\/span>\r\n<div data-type=\"newline\" data-count=\"2\">a. Let [latex]X[\/latex] = the number of days Nancy ____________________.<\/div>\r\n<div 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\">\u00a0b. [latex]X[\/latex] takes on what values?<\/div>\r\n<\/div>\r\n<\/section><\/div>\r\n<div 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\">\u00a0c. Suppose one week is randomly chosen. Construct a probability distribution table (called a PDF table) like the one in Example 1. 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><\/div>\r\n<\/div>\r\n&nbsp;\r\n\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=\"\"><header>\r\n<div class=\"textbox exercises\">\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=\"\"><header>\r\n<h3 class=\"title\" data-type=\"title\">Example<\/h3>\r\n<\/header><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 <em data-effect=\"italics\">X<\/em> and what values does it take on?<\/p>\r\nSolution:\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n<\/section><\/div>\r\n<\/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=\"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\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<\/div>\r\n<\/section><\/div>\r\n<\/section><\/div>\r\n<\/div>\r\n<\/div>\r\n&nbsp;\r\n\r\n<\/header><\/div>\r\n<\/div>\r\n<div id=\"fs-idm96796576\" class=\"note statistics try ui-has-child-title\" data-type=\"note\" data-has-label=\"true\" data-label=\"\"><section id=\"fs-idp97044640\" class=\"summary\" data-depth=\"1\">\r\n<h2 data-type=\"title\">Concept Review<\/h2>\r\n<p id=\"fs-idm43618304\">The characteristics of a probability distribution function (PDF) for a discrete random variable are as follows:<\/p>\r\n\r\n<ol id=\"fs-idm39706128\" data-number-style=\"arabic\">\r\n \t<li>Each probability is between zero and one, inclusive (<em data-effect=\"italics\">inclusive<\/em> means to include zero and one).<\/li>\r\n \t<li>The sum of the probabilities is one.<\/li>\r\n<\/ol>\r\n<\/section><section id=\"fs-idp69020960\" class=\"practice\" data-depth=\"1\">\r\n<div class=\"textbox key-takeaways\">\r\n<div id=\"fs-idm96796576\" class=\"note statistics try ui-has-child-title\" data-type=\"note\" data-has-label=\"true\" data-label=\"\"><section id=\"fs-idp69020960\" class=\"practice\" data-depth=\"1\">\r\n<h3 data-type=\"title\">\u00a0Try it<\/h3>\r\nSolution:\r\n\r\na. Let [latex]X[\/latex] = the number of days Nancy attends class per week.\r\n\r\n<\/section>b. [latex]0, 1, 2,[\/latex] and [latex]3[\/latex]\r\n\r\n<\/div>\r\n<div class=\"note statistics try ui-has-child-title\" data-type=\"note\" data-has-label=\"true\" data-label=\"\">\r\n<p id=\"eip-idp146953184\">c.<\/p>\r\n\r\n<table id=\"eip-idp64719200\" style=\"height: 55px;\" summary=\"PDF table of the number of times Nancy attends class per week and probabilities.\">\r\n<thead>\r\n<tr style=\"height: 11px;\">\r\n<th style=\"height: 11px; width: 149.656px;\">[latex]x[\/latex]<\/th>\r\n<th style=\"height: 11px; width: 180.656px;\">[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: 149.656px;\">[latex]0[\/latex]<\/td>\r\n<td style=\"height: 11px; width: 180.656px;\">[latex]0.01[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 11px;\">\r\n<td style=\"height: 11px; width: 149.656px;\">[latex]1[\/latex]<\/td>\r\n<td style=\"height: 11px; width: 180.656px;\">[latex]0.04[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 11px;\">\r\n<td style=\"height: 11px; width: 149.656px;\">[latex]2[\/latex]<\/td>\r\n<td style=\"height: 11px; width: 180.656px;\">[latex]0.15[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 11px;\">\r\n<td style=\"height: 11px; width: 149.656px;\">[latex]3[\/latex]<\/td>\r\n<td style=\"height: 11px; width: 180.656px;\">[latex]0.80[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/section><\/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>Recognize and understand discrete probability distribution functions, in general<\/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 id=\"enumprac\" data-number-style=\"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>[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<p>&nbsp;<\/p>\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 key-takeaways\">\n<h3 id=\"element-500\">Try it<\/h3>\n<p>Suppose Nancy has classes <strong>three days<\/strong> a week. She attends classes three days a week\u00a0<strong>[latex]80[\/latex]%<\/strong> of the time, <strong>two days <\/strong><strong>[latex]15[\/latex]%<\/strong>\u00a0of the time, <strong>one day [latex]4[\/latex]%<\/strong>\u00a0of the time, and <strong>no days [latex]1[\/latex]<\/strong><strong style=\"font-size: 1rem; text-align: initial;\">%\u00a0<\/strong><span style=\"font-size: 1rem; text-align: initial;\">of the time. Suppose one week is randomly selected.<\/span><\/p>\n<div data-type=\"newline\" data-count=\"2\">a. Let [latex]X[\/latex] = the number of days Nancy ____________________.<\/div>\n<div 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\">\u00a0b. [latex]X[\/latex] takes on what values?<\/div>\n<\/div>\n<\/section>\n<\/div>\n<div 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\">\u00a0c. Suppose one week is randomly chosen. Construct a probability distribution table (called a PDF table) like the one in Example 1. 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>\n<\/div>\n<p>&nbsp;<\/p>\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=\"\">\n<header>\n<div class=\"textbox exercises\">\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=\"\"><\/div>\n<\/div>\n<\/div>\n<\/header>\n<header>\n<h3 class=\"title\" data-type=\"title\">Example<\/h3>\n<\/header>\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 <em data-effect=\"italics\">X<\/em> and what values does it take on?<\/p>\n<p>Solution:<\/p>\n<\/div>\n<\/section>\n<\/div>\n<\/section>\n<\/div>\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=\"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>[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<\/section>\n<\/div>\n<\/section>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div id=\"fs-idm96796576\" class=\"note statistics try ui-has-child-title\" data-type=\"note\" data-has-label=\"true\" data-label=\"\">\n<section id=\"fs-idp97044640\" class=\"summary\" data-depth=\"1\">\n<h2 data-type=\"title\">Concept Review<\/h2>\n<p id=\"fs-idm43618304\">The characteristics of a probability distribution function (PDF) for a discrete random variable are as follows:<\/p>\n<ol id=\"fs-idm39706128\" data-number-style=\"arabic\">\n<li>Each probability is between zero and one, inclusive (<em data-effect=\"italics\">inclusive<\/em> means to include zero and one).<\/li>\n<li>The sum of the probabilities is one.<\/li>\n<\/ol>\n<\/section>\n<section id=\"fs-idp69020960\" class=\"practice\" data-depth=\"1\">\n<div class=\"textbox key-takeaways\">\n<div id=\"fs-idm96796576\" class=\"note statistics try ui-has-child-title\" data-type=\"note\" data-has-label=\"true\" data-label=\"\">\n<section id=\"fs-idp69020960\" class=\"practice\" data-depth=\"1\">\n<h3 data-type=\"title\">\u00a0Try it<\/h3>\n<p>Solution:<\/p>\n<p>a. Let [latex]X[\/latex] = the number of days Nancy attends class per week.<\/p>\n<\/section>\n<p>b. [latex]0, 1, 2,[\/latex] and [latex]3[\/latex]<\/p>\n<\/div>\n<div class=\"note statistics try ui-has-child-title\" data-type=\"note\" data-has-label=\"true\" data-label=\"\">\n<p id=\"eip-idp146953184\">c.<\/p>\n<table id=\"eip-idp64719200\" style=\"height: 55px;\" summary=\"PDF table of the number of times Nancy attends class per week and probabilities.\">\n<thead>\n<tr style=\"height: 11px;\">\n<th style=\"height: 11px; width: 149.656px;\">[latex]x[\/latex]<\/th>\n<th style=\"height: 11px; width: 180.656px;\">[latex]P(x)[\/latex]<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr style=\"height: 11px;\">\n<td style=\"height: 11px; width: 149.656px;\">[latex]0[\/latex]<\/td>\n<td style=\"height: 11px; width: 180.656px;\">[latex]0.01[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 11px;\">\n<td style=\"height: 11px; width: 149.656px;\">[latex]1[\/latex]<\/td>\n<td style=\"height: 11px; width: 180.656px;\">[latex]0.04[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 11px;\">\n<td style=\"height: 11px; width: 149.656px;\">[latex]2[\/latex]<\/td>\n<td style=\"height: 11px; width: 180.656px;\">[latex]0.15[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 11px;\">\n<td style=\"height: 11px; width: 149.656px;\">[latex]3[\/latex]<\/td>\n<td style=\"height: 11px; width: 180.656px;\">[latex]0.80[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/section>\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-148\">\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 Illowski, Susan Dean. <strong>Provided by<\/strong>: Open Stax. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/cnx.org\/contents\/30189442-6998-4686-ac05-ed152b91b9de@17.44\">http:\/\/cnx.org\/contents\/30189442-6998-4686-ac05-ed152b91b9de@17.44<\/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>: Download for free at http:\/\/cnx.org\/contents\/30189442-6998-4686-ac05-ed152b91b9de@17.44<\/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":21,"menu_order":2,"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 Illowski, Susan Dean\",\"organization\":\"Open Stax\",\"url\":\"http:\/\/cnx.org\/contents\/30189442-6998-4686-ac05-ed152b91b9de@17.44\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download for free at http:\/\/cnx.org\/contents\/30189442-6998-4686-ac05-ed152b91b9de@17.44\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-148","chapter","type-chapter","status-publish","hentry"],"part":145,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/ntcc-introstats1\/wp-json\/pressbooks\/v2\/chapters\/148","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/ntcc-introstats1\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/ntcc-introstats1\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ntcc-introstats1\/wp-json\/wp\/v2\/users\/21"}],"version-history":[{"count":10,"href":"https:\/\/courses.lumenlearning.com\/ntcc-introstats1\/wp-json\/pressbooks\/v2\/chapters\/148\/revisions"}],"predecessor-version":[{"id":2004,"href":"https:\/\/courses.lumenlearning.com\/ntcc-introstats1\/wp-json\/pressbooks\/v2\/chapters\/148\/revisions\/2004"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/ntcc-introstats1\/wp-json\/pressbooks\/v2\/parts\/145"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/ntcc-introstats1\/wp-json\/pressbooks\/v2\/chapters\/148\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/ntcc-introstats1\/wp-json\/wp\/v2\/media?parent=148"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ntcc-introstats1\/wp-json\/pressbooks\/v2\/chapter-type?post=148"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ntcc-introstats1\/wp-json\/wp\/v2\/contributor?post=148"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ntcc-introstats1\/wp-json\/wp\/v2\/license?post=148"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}