{"id":1270,"date":"2021-08-23T18:33:44","date_gmt":"2021-08-23T18:33:44","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/?post_type=chapter&#038;p=1270"},"modified":"2023-12-05T09:07:54","modified_gmt":"2023-12-05T09:07:54","slug":"summary-probability-distribution-function-pdf-for-a-discrete-random-variable","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/chapter\/summary-probability-distribution-function-pdf-for-a-discrete-random-variable\/","title":{"raw":"Summary: Probability Distribution Function (PDF) for a Discrete Random Variable","rendered":"Summary: Probability Distribution Function (PDF) for a Discrete Random Variable"},"content":{"raw":"<h2>Key Concepts<\/h2>\r\n<ul>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">The probability for each value in a probability distribution is between 0 and 1, inclusive.<\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">The sum of the probabilities in a probability distribution is 1.<\/li>\r\n<\/ul>\r\n<h2>Glossary<\/h2>\r\n<strong>probability distribution function (PDF):\u00a0<\/strong>a mathematical description of a discrete random variable (RV), given either in the form of an equation (formula) or in the form of a table listing all the possible outcomes of an experiment and the probability associated with each outcome.\r\n\r\n<strong>random variable (RV):\u00a0<\/strong>a characteristic of interest in a population being studied; common notation for variables are upper case Latin letters [latex]X, Y, Z,[\/latex]...; common notation for a specific value from the domain (set of all possible values of a variable) are lower case Latin letters [latex]x, y, and z[\/latex]. For example, if [latex]X[\/latex] is the number of children in a family, then [latex]x[\/latex] represents a specific integer [latex]0, 1, 2, 3,[\/latex].... Variables in statistics differ from variables in intermediate algebra in the two following ways:\r\n<ul>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">The domain of the random variable (RV) is not necessarily a numerical set; the domain may be expressed in words; for example, if [latex]X=[\/latex] hair color then the domain is {black, blond, gray, green, orange}.<\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">We can tell what specific value [latex]x[\/latex] the random variable [latex]X[\/latex] takes only after performing the experiment.<\/li>\r\n<\/ul>","rendered":"<h2>Key Concepts<\/h2>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\">The probability for each value in a probability distribution is between 0 and 1, inclusive.<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">The sum of the probabilities in a probability distribution is 1.<\/li>\n<\/ul>\n<h2>Glossary<\/h2>\n<p><strong>probability distribution function (PDF):\u00a0<\/strong>a mathematical description of a discrete random variable (RV), given either in the form of an equation (formula) or in the form of a table listing all the possible outcomes of an experiment and the probability associated with each outcome.<\/p>\n<p><strong>random variable (RV):\u00a0<\/strong>a characteristic of interest in a population being studied; common notation for variables are upper case Latin letters [latex]X, Y, Z,[\/latex]&#8230;; common notation for a specific value from the domain (set of all possible values of a variable) are lower case Latin letters [latex]x, y, and z[\/latex]. For example, if [latex]X[\/latex] is the number of children in a family, then [latex]x[\/latex] represents a specific integer [latex]0, 1, 2, 3,[\/latex]&#8230;. Variables in statistics differ from variables in intermediate algebra in the two following ways:<\/p>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\">The domain of the random variable (RV) is not necessarily a numerical set; the domain may be expressed in words; for example, if [latex]X=[\/latex] hair color then the domain is {black, blond, gray, green, orange}.<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">We can tell what specific value [latex]x[\/latex] the random variable [latex]X[\/latex] takes only after performing the experiment.<\/li>\n<\/ul>\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-1270\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li><strong>Provided by<\/strong>: Lumen Learning. <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 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>: OpenStax. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/openstax.org\/books\/introductory-statistics\/pages\/4-key-terms\">https:\/\/openstax.org\/books\/introductory-statistics\/pages\/4-key-terms<\/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>\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":9,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Introductory Statistics\",\"author\":\"Barbara Illowsky, Susan Dean\",\"organization\":\"OpenStax\",\"url\":\"https:\/\/openstax.org\/books\/introductory-statistics\/pages\/4-key-terms\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Access for free at https:\/\/openstax.org\/books\/introductory-statistics\/pages\/1-introduction\"},{\"type\":\"original\",\"description\":\"\",\"author\":\"\",\"organization\":\"Lumen Learning\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-1270","chapter","type-chapter","status-publish","hentry"],"part":240,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/1270","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":3,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/1270\/revisions"}],"predecessor-version":[{"id":3507,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/1270\/revisions\/3507"}],"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\/1270\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/media?parent=1270"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapter-type?post=1270"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/contributor?post=1270"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/license?post=1270"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}