{"id":1304,"date":"2021-08-23T20:10:06","date_gmt":"2021-08-23T20:10:06","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/?post_type=chapter&#038;p=1304"},"modified":"2023-12-05T09:12:24","modified_gmt":"2023-12-05T09:12:24","slug":"summary-poisson-distribution","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/chapter\/summary-poisson-distribution\/","title":{"raw":"Summary: Poisson Distribution","rendered":"Summary: Poisson Distribution"},"content":{"raw":"<h2>Key Concepts<\/h2>\r\n<ul>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">A Poisson distribution is a discrete random variable.<\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">Calculating a Poisson probability is based on the average number of occurrences for a specific interval of time.<\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">For a Poisson distribution, the chances of the event happening are independent of when the event previously happened.<\/li>\r\n<\/ul>\r\n<h2>Glossary<\/h2>\r\n<strong>Poisson probability distribution:\u00a0<\/strong>a discrete random variable [latex](RV)[\/latex] that counts the number of times a certain event will occur in a specific interval; characteristics of the variable:\r\n<ul>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">The probability that the event occurs in a given interval is the same for all intervals.<\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">The events occur with a known mean and independently of the time since the last event.<\/li>\r\n<\/ul>\r\nThe distribution is defined by the mean\u00a0[latex]\\mu[\/latex] of the event in the interval. Notation: [latex]X \\sim P(\u03bc)[\/latex].\r\n\r\nThis mean is [latex]\\mu =np[\/latex]. The. standard deviation is [latex]\\sigma = \\sqrt{\\mu}[\/latex]. The probability of having exactly [latex]x[\/latex] successes. in [latex]r[\/latex] trials is [latex]P(X=x)=e^{- \\mu} (\\frac{\\mu^{x}}{x!})[\/latex]. The Poisson distribution is often used to approximate the binomial distribution, when [latex]n[\/latex] is \u201clarge\u201d and [latex]p[\/latex] is \u201csmall\u201d (a general rule is that [latex]n[\/latex] should be greater than or equal to 20 and [latex]p[\/latex] should be less than or equal to 0.05).","rendered":"<h2>Key Concepts<\/h2>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\">A Poisson distribution is a discrete random variable.<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">Calculating a Poisson probability is based on the average number of occurrences for a specific interval of time.<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">For a Poisson distribution, the chances of the event happening are independent of when the event previously happened.<\/li>\n<\/ul>\n<h2>Glossary<\/h2>\n<p><strong>Poisson probability distribution:\u00a0<\/strong>a discrete random variable [latex](RV)[\/latex] that counts the number of times a certain event will occur in a specific interval; characteristics of the variable:<\/p>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\">The probability that the event occurs in a given interval is the same for all intervals.<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">The events occur with a known mean and independently of the time since the last event.<\/li>\n<\/ul>\n<p>The distribution is defined by the mean\u00a0[latex]\\mu[\/latex] of the event in the interval. Notation: [latex]X \\sim P(\u03bc)[\/latex].<\/p>\n<p>This mean is [latex]\\mu =np[\/latex]. The. standard deviation is [latex]\\sigma = \\sqrt{\\mu}[\/latex]. The probability of having exactly [latex]x[\/latex] successes. in [latex]r[\/latex] trials is [latex]P(X=x)=e^{- \\mu} (\\frac{\\mu^{x}}{x!})[\/latex]. The Poisson distribution is often used to approximate the binomial distribution, when [latex]n[\/latex] is \u201clarge\u201d and [latex]p[\/latex] is \u201csmall\u201d (a general rule is that [latex]n[\/latex] should be greater than or equal to 20 and [latex]p[\/latex] should be less than or equal to 0.05).<\/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-1304\">\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":28,"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-1304","chapter","type-chapter","status-publish","hentry"],"part":240,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/1304","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\/1304\/revisions"}],"predecessor-version":[{"id":3589,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/1304\/revisions\/3589"}],"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\/1304\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/media?parent=1304"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapter-type?post=1304"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/contributor?post=1304"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/license?post=1304"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}