{"id":237,"date":"2023-12-21T10:58:33","date_gmt":"2023-12-21T15:58:33","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/?post_type=part&#038;p=237"},"modified":"2024-07-24T10:19:16","modified_gmt":"2024-07-24T14:19:16","slug":"intro-to-inferential-statistics","status":"publish","type":"part","link":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/part\/intro-to-inferential-statistics\/","title":{"raw":"Poisson Distributions","rendered":"Poisson Distributions"},"content":{"raw":"<h2>Poisson Probability Distributions<\/h2>\r\nIn this section, we examine Poisson Probability Distributions:\r\n\r\n[caption id=\"attachment_1673\" align=\"alignnone\" width=\"1043\"]<a href=\"https:\/\/www.wolframalpha.com\/input?i=graph+poisson+distribution\" target=\"_blank\" rel=\"noopener\"><img class=\"wp-image-1673 size-full\" title=\"https:\/\/www.wolframalpha.com\/input?i=graph+poisson+distribution\" src=\"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2023\/12\/Poisson_Graphs.jpg\" alt=\"Graphs of Poisson Distribution for an average of 2, 7, and 12\" width=\"1043\" height=\"226\" \/><\/a> Graphs of poisson distributions for different averages (\u03bb)[\/caption]\r\n<ul>\r\n \t<li>They are continuous distributions<\/li>\r\n \t<li>They measure the probability of a certain number, [latex]x[\/latex], events occurring over a certain time period<\/li>\r\n<\/ul>\r\n<h2>The sections are organized as follows:<\/h2>\r\n<ol>\r\n \t<li>An introduction, properties of Poisson Distributions and how to calculate the probability of exactly [latex]x[\/latex] events occurring.<\/li>\r\n \t<li>How to change lambda ([latex]\\lambda[\/latex]) when the time interval in the question differs from the one stated for the average.<\/li>\r\n \t<li>How to calculate the probability of at least, at most or more than [latex]x[\/latex] events occurring during a time interval.<\/li>\r\n \t<li>How to calculate the mean and standard deviation for Poisson distributions.<\/li>\r\n<\/ol>","rendered":"<h2>Poisson Probability Distributions<\/h2>\n<p>In this section, we examine Poisson Probability Distributions:<\/p>\n<figure id=\"attachment_1673\" aria-describedby=\"caption-attachment-1673\" style=\"width: 1043px\" class=\"wp-caption alignnone\"><a href=\"https:\/\/www.wolframalpha.com\/input?i=graph+poisson+distribution\" target=\"_blank\" rel=\"noopener\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1673 size-full\" title=\"https:\/\/www.wolframalpha.com\/input?i=graph+poisson+distribution\" src=\"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2023\/12\/Poisson_Graphs.jpg\" alt=\"Graphs of Poisson Distribution for an average of 2, 7, and 12\" width=\"1043\" height=\"226\" srcset=\"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2023\/12\/Poisson_Graphs.jpg 1043w, https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2023\/12\/Poisson_Graphs-300x65.jpg 300w, https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2023\/12\/Poisson_Graphs-1024x222.jpg 1024w, https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2023\/12\/Poisson_Graphs-768x166.jpg 768w, https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2023\/12\/Poisson_Graphs-65x14.jpg 65w, https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2023\/12\/Poisson_Graphs-225x49.jpg 225w, https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2023\/12\/Poisson_Graphs-350x76.jpg 350w\" sizes=\"auto, (max-width: 1043px) 100vw, 1043px\" \/><\/a><figcaption id=\"caption-attachment-1673\" class=\"wp-caption-text\">Graphs of poisson distributions for different averages (\u03bb)<\/figcaption><\/figure>\n<ul>\n<li>They are continuous distributions<\/li>\n<li>They measure the probability of a certain number, [latex]x[\/latex], events occurring over a certain time period<\/li>\n<\/ul>\n<h2>The sections are organized as follows:<\/h2>\n<ol>\n<li>An introduction, properties of Poisson Distributions and how to calculate the probability of exactly [latex]x[\/latex] events occurring.<\/li>\n<li>How to change lambda ([latex]\\lambda[\/latex]) when the time interval in the question differs from the one stated for the average.<\/li>\n<li>How to calculate the probability of at least, at most or more than [latex]x[\/latex] events occurring during a time interval.<\/li>\n<li>How to calculate the mean and standard deviation for Poisson distributions.<\/li>\n<\/ol>\n","protected":false},"parent":0,"menu_order":6,"template":"","meta":{"pb_part_invisible":false,"pb_part_invisible_string":""},"contributor":[],"license":[],"class_list":["post-237","part","type-part","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/pressbooks\/v2\/parts\/237","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/pressbooks\/v2\/parts"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/wp\/v2\/types\/part"}],"version-history":[{"count":14,"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/pressbooks\/v2\/parts\/237\/revisions"}],"predecessor-version":[{"id":2503,"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/pressbooks\/v2\/parts\/237\/revisions\/2503"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/wp\/v2\/media?parent=237"}],"wp:term":[{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/wp\/v2\/contributor?post=237"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/wp\/v2\/license?post=237"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}