{"id":180012,"date":"2024-01-07T04:22:33","date_gmt":"2024-01-07T10:22:33","guid":{"rendered":"https:\/\/lifeboat.com\/blog\/2024\/01\/bernoulli-trial"},"modified":"2024-01-07T04:22:33","modified_gmt":"2024-01-07T10:22:33","slug":"bernoulli-trial","status":"publish","type":"post","link":"https:\/\/lifeboat.com\/blog\/2024\/01\/bernoulli-trial","title":{"rendered":"Bernoulli trial"},"content":{"rendered":"<p><a class=\"aligncenter blog-photo\" href=\"https:\/\/lifeboat.com\/blog.images\/bernoulli-trial2.jpg\"><\/a><\/p>\n<p>A #mathematics \u201cA Bernoulli trial is a #random experiment with exactly two possible outcomes \u201c<i>success<\/i>\u201d and \u201cfailure\u201d in which #probability of <i>success<\/i> is the same every time the experiment is conducted.\u201d<\/p>\n<hr>\n<p>In the theory of <a href=\"https:\/\/en.wikipedia.org\/wiki\/Probability\" title=\"Probability\">probability<\/a> and <a href=\"https:\/\/en.wikipedia.org\/wiki\/Statistics\" title=\"Statistics\">statistics<\/a>, a <b>Bernoulli trial<\/b> (or <b>binomial trial<\/b>) is a random <a href=\"https:\/\/en.wikipedia.org\/wiki\/Experiment_(probability_theory)\" title=\"Experiment (probability theory)\">experiment<\/a> with exactly two possible <a href=\"https:\/\/en.wikipedia.org\/wiki\/Outcome_(probability)\" title=\"Outcome (probability)\">outcomes<\/a>, \u201c<i>success<\/i>\u201d and \u201cfailure\u201d, in which the probability of <i>success<\/i> is the same every time the experiment is conducted.<sup id=\u201d cite_ref-1\u201d class=\u201d reference\u201d>[1]<\/sup> It is named after <a href=\"https:\/\/en.wikipedia.org\/wiki\/Jacob_Bernoulli\" title=\"Jacob Bernoulli\">Jacob Bernoulli<\/a>, a 17th-century Swiss mathematician, who analyzed them in his <i lang=\"la\"><a href=\"https:\/\/en.wikipedia.org\/wiki\/Ars_Conjectandi\" title=\"Ars Conjectandi\">Ars Conjectandi<\/a> <\/i> (1713).<sup id=\u201d cite_ref-2\u201d class=\u201d reference\u201d>[2]<\/sup><\/p>\n<p>The mathematical formalisation of the Bernoulli trial is known as the <a href=\"https:\/\/en.wikipedia.org\/wiki\/Bernoulli_process\" title=\"Bernoulli process\">Bernoulli process<\/a>. This article offers an elementary introduction to the concept, whereas the article on the Bernoulli process offers a more advanced treatment.<\/p>\n<p>Since a Bernoulli trial has only two possible outcomes, it can be framed as some \u201cyes or no\u201d question. For example:<\/p>\n","protected":false},"excerpt":{"rendered":"<p>A #mathematics \u201cA Bernoulli trial is a #random experiment with exactly two possible outcomes \u201csuccess\u201d and \u201cfailure\u201d in which #probability of success is the same every time the experiment is conducted.\u201d In the theory of probability and statistics, a Bernoulli trial (or binomial trial) is a random experiment with exactly two possible outcomes, \u201csuccess\u201d and [\u2026]<\/p>\n","protected":false},"author":709,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2229],"tags":[],"class_list":["post-180012","post","type-post","status-publish","format-standard","hentry","category-mathematics"],"_links":{"self":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts\/180012","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/users\/709"}],"replies":[{"embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/comments?post=180012"}],"version-history":[{"count":0,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts\/180012\/revisions"}],"wp:attachment":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/media?parent=180012"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/categories?post=180012"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/tags?post=180012"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}