{"id":1299,"date":"2021-08-23T20:02:09","date_gmt":"2021-08-23T20:02:09","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/?post_type=chapter&#038;p=1299"},"modified":"2023-12-05T09:11:21","modified_gmt":"2023-12-05T09:11:21","slug":"summary-hypergeometric-distribution","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/chapter\/summary-hypergeometric-distribution\/","title":{"raw":"Summary: Hypergeometric Distribution","rendered":"Summary: Hypergeometric Distribution"},"content":{"raw":"<h2>Key Concepts<\/h2>\r\n<ul>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">A hypergeometric distribution does not consist of Bernoulli trials.<\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">In a hypergeometric experiment, the probability of \u201csuccess\u201d is not the same, because sampling is done without replacement, which means each selection is not independent.<\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">The number of trials in a hypergeometric experiment is fixed.<\/li>\r\n<\/ul>\r\n<h2>Glossary<\/h2>\r\n<strong>hypergeometric experiment:<\/strong> a statistical experiment with the following properties:\r\n<ol>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">You take samples from two groups.<\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">You are concerned with a group of interest, called the first group.<\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">You sample without replacement from the combined groups.<\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">Each pick is not independent, since sampling is without replacement.<\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">You are not dealing with Bernoulli Trials.<\/li>\r\n<\/ol>\r\n<strong>hypergeometric probability:\u00a0<\/strong>a discrete random variable [latex](RV)[\/latex] that is characterized by:\r\n<ol>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">A fixed number of trials.<\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">The probability of success is not the same from trial to trial.<\/li>\r\n<\/ol>\r\nWe sample from two groups of items when we are interested in only one group. [latex]X[\/latex] is defined as the number of successes out of the total number of items chosen. Notation: [latex]X \\sim H(r, b, n)[\/latex], where [latex]r =[\/latex] the number of items in the group of interest, [latex]b =[\/latex] the number of items in the group not of interest, and [latex]n =[\/latex] the number of items chosen.","rendered":"<h2>Key Concepts<\/h2>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\">A hypergeometric distribution does not consist of Bernoulli trials.<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">In a hypergeometric experiment, the probability of \u201csuccess\u201d is not the same, because sampling is done without replacement, which means each selection is not independent.<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">The number of trials in a hypergeometric experiment is fixed.<\/li>\n<\/ul>\n<h2>Glossary<\/h2>\n<p><strong>hypergeometric experiment:<\/strong> a statistical experiment with the following properties:<\/p>\n<ol>\n<li style=\"font-weight: 400;\" aria-level=\"1\">You take samples from two groups.<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">You are concerned with a group of interest, called the first group.<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">You sample without replacement from the combined groups.<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">Each pick is not independent, since sampling is without replacement.<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">You are not dealing with Bernoulli Trials.<\/li>\n<\/ol>\n<p><strong>hypergeometric probability:\u00a0<\/strong>a discrete random variable [latex](RV)[\/latex] that is characterized by:<\/p>\n<ol>\n<li style=\"font-weight: 400;\" aria-level=\"1\">A fixed number of trials.<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">The probability of success is not the same from trial to trial.<\/li>\n<\/ol>\n<p>We sample from two groups of items when we are interested in only one group. [latex]X[\/latex] is defined as the number of successes out of the total number of items chosen. Notation: [latex]X \\sim H(r, b, n)[\/latex], where [latex]r =[\/latex] the number of items in the group of interest, [latex]b =[\/latex] the number of items in the group not of interest, and [latex]n =[\/latex] the number of items chosen.<\/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-1299\">\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":24,"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-1299","chapter","type-chapter","status-publish","hentry"],"part":240,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/1299","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\/1299\/revisions"}],"predecessor-version":[{"id":3581,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/1299\/revisions\/3581"}],"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\/1299\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/media?parent=1299"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapter-type?post=1299"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/contributor?post=1299"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/license?post=1299"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}