{"id":917,"date":"2017-04-20T05:17:20","date_gmt":"2017-04-20T05:17:20","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/?post_type=chapter&#038;p=917"},"modified":"2019-06-28T15:33:19","modified_gmt":"2019-06-28T15:33:19","slug":"introduction-discrete-probability-distribution","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/chapter\/introduction-discrete-probability-distribution\/","title":{"raw":"Introduction to Discrete Probability Distribution","rendered":"Introduction to Discrete Probability Distribution"},"content":{"raw":"<h2>What you'll learn to do: Use probability distributions for discrete and continuous random variables to estimate probabilities and identify unusual events.<\/h2>\r\n<img class=\"size-medium wp-image-2030 alignright\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1768\/2017\/04\/28153213\/Number-of-Majors-Changed-300x200.png\" alt=\"Probability histogram of number of changes in major, with the higher bars in 1 change and 2 changes\" width=\"300\" height=\"200\" \/>\r\n\r\nIn studying a probability experiment, it is often useful to work with quantitative values to represent outcomes. These quantitative values associated to outcomes are called random variables. In this section, we explore random variables that take on numeric values that can be listed.\u00a0 For example, number of books is a discrete random variable. On the other hand, hair color is not a random variable because hair color is not numeric. Also, any decimal between 0 and 1 is not discrete because we cannot list out all the decimals. In analyzing real life data, we will apply fundamental concepts about discrete probability distributions to estimate likelihoods and draw inferences.\r\n<h2>Contribute!<\/h2><div style=\"margin-bottom: 8px;\">Did you have an idea for improving this content? We\u2019d love your input.<\/div><a href=\"https:\/\/docs.google.com\/document\/d\/1VaR-6FfcbgBmvHCYj_UFNyu7w-BdDvKOC_7HwZSDIYI\" target=\"_blank\" style=\"font-size: 10pt; font-weight: 600; color: #077fab; text-decoration: none; border: 2px solid #077fab; border-radius: 7px; padding: 5px 25px; text-align: center; cursor: pointer; line-height: 1.5em;\">Improve this page<\/a><a style=\"margin-left: 16px;\" target=\"_blank\" href=\"https:\/\/docs.google.com\/document\/d\/1vy-T6DtTF-BbMfpVEI7VP_R7w2A4anzYZLXR8Pk4Fu4\">Learn More<\/a>","rendered":"<h2>What you&#8217;ll learn to do: Use probability distributions for discrete and continuous random variables to estimate probabilities and identify unusual events.<\/h2>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-medium wp-image-2030 alignright\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1768\/2017\/04\/28153213\/Number-of-Majors-Changed-300x200.png\" alt=\"Probability histogram of number of changes in major, with the higher bars in 1 change and 2 changes\" width=\"300\" height=\"200\" \/><\/p>\n<p>In studying a probability experiment, it is often useful to work with quantitative values to represent outcomes. These quantitative values associated to outcomes are called random variables. In this section, we explore random variables that take on numeric values that can be listed.\u00a0 For example, number of books is a discrete random variable. On the other hand, hair color is not a random variable because hair color is not numeric. Also, any decimal between 0 and 1 is not discrete because we cannot list out all the decimals. In analyzing real life data, we will apply fundamental concepts about discrete probability distributions to estimate likelihoods and draw inferences.<\/p>\n<h2>Contribute!<\/h2>\n<div style=\"margin-bottom: 8px;\">Did you have an idea for improving this content? We\u2019d love your input.<\/div>\n<p><a href=\"https:\/\/docs.google.com\/document\/d\/1VaR-6FfcbgBmvHCYj_UFNyu7w-BdDvKOC_7HwZSDIYI\" target=\"_blank\" style=\"font-size: 10pt; font-weight: 600; color: #077fab; text-decoration: none; border: 2px solid #077fab; border-radius: 7px; padding: 5px 25px; text-align: center; cursor: pointer; line-height: 1.5em;\">Improve this page<\/a><a style=\"margin-left: 16px;\" target=\"_blank\" href=\"https:\/\/docs.google.com\/document\/d\/1vy-T6DtTF-BbMfpVEI7VP_R7w2A4anzYZLXR8Pk4Fu4\">Learn More<\/a><\/p>\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-917\">\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>Concepts in Statistics. <strong>Provided by<\/strong>: Open Learning Initiative. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/oli.cmu.edu\">http:\/\/oli.cmu.edu<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/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":163,"menu_order":9,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Concepts in Statistics\",\"author\":\"\",\"organization\":\"Open Learning Initiative\",\"url\":\"http:\/\/oli.cmu.edu\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"8f648af7-5196-4bb9-ad2c-dfac537bff39","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-917","chapter","type-chapter","status-publish","hentry"],"part":258,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/wp-json\/pressbooks\/v2\/chapters\/917","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/wp-json\/wp\/v2\/users\/163"}],"version-history":[{"count":8,"href":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/wp-json\/pressbooks\/v2\/chapters\/917\/revisions"}],"predecessor-version":[{"id":2032,"href":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/wp-json\/pressbooks\/v2\/chapters\/917\/revisions\/2032"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/wp-json\/pressbooks\/v2\/parts\/258"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/wp-json\/pressbooks\/v2\/chapters\/917\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/wp-json\/wp\/v2\/media?parent=917"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/wp-json\/pressbooks\/v2\/chapter-type?post=917"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/wp-json\/wp\/v2\/contributor?post=917"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/wp-json\/wp\/v2\/license?post=917"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}