{"id":220,"date":"2023-08-04T00:49:55","date_gmt":"2023-08-04T00:49:55","guid":{"rendered":"https:\/\/statorials.org\/pt\/distribuicao-bernoulli\/"},"modified":"2023-08-04T00:49:55","modified_gmt":"2023-08-04T00:49:55","slug":"distribuicao-bernoulli","status":"publish","type":"post","link":"https:\/\/statorials.org\/pt\/distribuicao-bernoulli\/","title":{"rendered":"Distribui\u00e7\u00e3o bernoulli"},"content":{"rendered":"<p>Este artigo explica o que \u00e9 a distribui\u00e7\u00e3o de Bernoulli e qual \u00e9 sua f\u00f3rmula. Al\u00e9m disso, voc\u00ea encontrar\u00e1 as propriedades da distribui\u00e7\u00e3o de Bernoulli e um exerc\u00edcio resolvido para entender melhor seu significado. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-distribucion-de-bernoulli\"><\/span> Qual \u00e9 a distribui\u00e7\u00e3o de Bernoulli?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> A <strong>distribui\u00e7\u00e3o de Bernoulli<\/strong> , tamb\u00e9m conhecida como <strong>distribui\u00e7\u00e3o dicot\u00f4mica<\/strong> , \u00e9 uma distribui\u00e7\u00e3o de probabilidade que representa uma vari\u00e1vel discreta que s\u00f3 pode ter dois resultados: \u201csucesso\u201d ou \u201cfracasso\u201d.<\/p>\n<p> Na distribui\u00e7\u00e3o de Bernoulli, \u201csucesso\u201d \u00e9 o resultado que esperamos e tem o valor 1, enquanto o resultado de \u201cfracasso\u201d \u00e9 um resultado diferente do esperado e tem o valor 0. Portanto, se a probabilidade do resultado de \u201c sucesso\u201d \u00e9 <em>p<\/em> , a probabilidade do resultado de \u201cfracasso\u201d \u00e9 <em>q=1-p<\/em> .<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-384fd7d96d4d6584739b04a6e331b251_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}X\\sim \\text{Bernoulli}(p)\\\\[2ex]\\begin{array}{l} \\text{\\'Exito}\\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ P[X=1]=p\\\\[2ex]\\text{Fracaso}\\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ P[X=0]=q=1-p\\end{array}\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"95\" width=\"361\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> A distribui\u00e7\u00e3o de Bernoulli recebeu o nome do estat\u00edstico su\u00ed\u00e7o Jacob Bernoulli.<\/p>\n<p> Em estat\u00edstica, a distribui\u00e7\u00e3o de Bernoulli tem principalmente uma aplica\u00e7\u00e3o: definir as probabilidades de experi\u00eancias nas quais existem apenas dois resultados poss\u00edveis: sucesso e fracasso. Portanto, um experimento que usa a distribui\u00e7\u00e3o de Bernoulli \u00e9 chamado de teste de Bernoulli ou experimento de Bernoulli. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-distribucion-de-bernoulli\"><\/span> F\u00f3rmula de distribui\u00e7\u00e3o de Bernoulli<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Se <em>p<\/em> for a probabilidade de ocorr\u00eancia do resultado de &#8220;sucesso&#8221;, a probabilidade da distribui\u00e7\u00e3o de Bernoulli \u00e9 igual a <em>p<\/em> elevado a <em>x<\/em> multiplicado por <em>1-p<\/em> elevado a <em>1-x<\/em> . Assim <strong>, as probabilidades da distribui\u00e7\u00e3o de Bernoulli podem ser calculadas utilizando a seguinte f\u00f3rmula<\/strong> : <\/p>\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/formule-de-distribution-bernouilli.png\" alt=\"F\u00f3rmula de distribui\u00e7\u00e3o de Bernoulli\" class=\"wp-image-4403\" width=\"266\" height=\"210\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p> Observe que em uma distribui\u00e7\u00e3o de Bernoulli, o valor de <em>x<\/em> s\u00f3 pode ser 0 (fracasso) ou 1 (sucesso).<\/p>\n<p> Por outro lado, a f\u00f3rmula anterior tamb\u00e9m pode ser escrita utilizando a seguinte express\u00e3o equivalente: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-ec9d35bd206499e27579d7c65d915a67_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\" \\displaystyle P[X=x]=\\left\\{\\begin{array}{ll}1-p &amp; \\text{si } x=0\\\\[2ex]p&amp; \\text{si } x=1\\end{array}\\right.\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"237\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-de-la-distribucion-de-bernoulli\"><\/span> Exemplo de distribui\u00e7\u00e3o de Bernoulli<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Agora que sabemos a defini\u00e7\u00e3o da distribui\u00e7\u00e3o de Bernoulli e qual \u00e9 a sua f\u00f3rmula, vamos ver um exemplo concreto da distribui\u00e7\u00e3o de Bernoulli.<\/p>\n<ul>\n<li> Para ganhar um jogo, o jogador deve lan\u00e7ar um dado e obter um 2, caso contr\u00e1rio outro jogador vencer\u00e1 o jogo e, portanto, o jogo ser\u00e1 perdido. Calcule a probabilidade de sucesso e fracasso.<\/li>\n<\/ul>\n<p> Um dado tem seis resultados poss\u00edveis (1, 2, 3, 4, 5, 6), ent\u00e3o, neste caso, o espa\u00e7o amostral do experimento \u00e9:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-b3ad0ac057b6cd7e3d3db78b556249a1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\Omega=\\{1,2,3,4,5,6\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"146\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> No nosso caso, o \u00fanico caso de sucesso \u00e9 obter o n\u00famero dois, portanto a probabilidade de sucesso ao aplicar a regra de Laplace \u00e9 igual a um dividido pelo n\u00famero total de resultados poss\u00edveis (6):<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-d3edc23a0939657deeeed11600ba29be_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"p=\\cfrac{1}{6}=0,1667\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"121\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Por outro lado, se aparecer outro n\u00famero ao lan\u00e7ar o dado, o resultado do experimento ser\u00e1 considerado um fracasso, pois o jogador perder\u00e1 o jogo. Assim, esta probabilidade \u00e9 equivalente a um menos a probabilidade calculada anteriormente:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-e227d2af05b593a352cc6cbd5481469c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"q=1-p=1-\\cfrac{1}{6}=\\cfrac{5}{6}=0,8333\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"247\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Resumindo, a distribui\u00e7\u00e3o de Bernoulli deste experimento \u00e9 definida pela seguinte express\u00e3o:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-440d054ce5c566fe8dd15f52c5f32059_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\" \\displaystyle P[X=x]=\\left\\{\\begin{array}{ll}\\cfrac{5}{6} &amp; \\text{si } x=0\\\\[4ex]\\cfrac{1}{6} &amp; \\text{si } x=1\\end{array}\\right.\" title=\"Rendered by QuickLaTeX.com\" height=\"108\" width=\"209\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Como voc\u00ea pode ver abaixo, as probabilidades da distribui\u00e7\u00e3o de Bernoulli tamb\u00e9m podem ser encontradas aplicando a f\u00f3rmula vista acima: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-cbe5fae22a9fc6271a376d76e7149c7d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P[X=x]=p^x\\cdot (1-p)^{1-x}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"207\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-847c03e1b95832f2100baaaf984bad98_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle P[X=0]=\\left(\\frac{1}{6}\\right)^0\\cdot \\left(1-\\frac{1}{6}\\right)^{1-0}=\\cfrac{5}{6}\" title=\"Rendered by QuickLaTeX.com\" height=\"47\" width=\"284\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-f2925f101c2a1cf6f9a5690b79265ba2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle P[X=1]=\\left(\\frac{1}{6}\\right)^1\\cdot \\left(1-\\frac{1}{6}\\right)^{1-1}=\\cfrac{1}{6}\" title=\"Rendered by QuickLaTeX.com\" height=\"47\" width=\"284\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"caracteristicas-de-la-distribucion-de-bernoulli\"><\/span> Caracter\u00edsticas da distribui\u00e7\u00e3o Bernoulli<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Abaixo est\u00e3o as caracter\u00edsticas mais importantes da distribui\u00e7\u00e3o Bernoulli.<\/p>\n<ul>\n<li> A distribui\u00e7\u00e3o de Bernoulli s\u00f3 pode assumir o valor 1 (sucesso) ou 0 (fracasso).<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-68118c3a558ed7a1de8983eda3baee86_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=\\{0\\ ; 1\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"82\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> A m\u00e9dia da distribui\u00e7\u00e3o de Bernoulli \u00e9 equivalente \u00e0 probabilidade de ocorr\u00eancia do resultado \u201csucesso\u201d.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-2b30550c767b243e13eaa5e05058cf40_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"E[X]=p\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"73\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> A vari\u00e2ncia de uma distribui\u00e7\u00e3o de Bernoulli pode ser calculada multiplicando as probabilidades de ocorr\u00eancia do resultado \u201csucesso\u201d e \u201cfracasso\u201d. Ou, de forma equivalente, a vari\u00e2ncia \u00e9 <em>p<\/em> vezes <em>1-p<\/em> .<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-8dd0da3524a93c4fc809dc9a7f8f9d8b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Var(X)=p\\cdot q=p\\cdot (1-p)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"214\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> O valor da moda de uma distribui\u00e7\u00e3o de Bernoulli depende das probabilidades de \u201csucesso\u201d e \u201cfracasso\u201d. Assim, a moda deste tipo de distribui\u00e7\u00e3o \u00e9 definida pela seguinte express\u00e3o:<\/li>\n<\/ul>\n<pre class=\"ql-errors\"> *** QuickLaTeX cannot compile formula:\n\\displaystyle Mo=\\left\\{\\begin{array}{ll}0 &amp; \\text{si } q&gt;p\\\\[2ex]0 \\ ;1 &amp; \\text{si } q=p\\\\[2ex] 1 &amp; \\text{si } q&lt;ul&gt;&lt;li&gt; The formula for the probability function of a Bernoulli distribution is as follows:&lt;\/li&gt;&lt;\/ul&gt;[latex] \\displaystyle P[X=x]= \\left\\{\\begin{array}{ll}1-p &amp; \\text{si } x=0\\\\[2ex]p&amp; \\text{si } x=1\\end{array}\\right.\n\n*** Error message:\nMissing $ inserted.\nleading text: \\displaystyle\nPlease use \\mathaccent for accents in math mode.\nleading text: ...&gt; The formula for the probability function\n\\begin{array} on input line 8 ended by \\end{document}.\nleading text: \\end{document}\nImproper \\prevdepth.\nleading text: \\end{document}\nMissing $ inserted.\nleading text: \\end{document}\nMissing } inserted.\nleading text: \\end{document}\nMissing \\cr inserted.\nleading text: \\end{document}\nMissing $ inserted.\nleading text: \\end{document}\nYou can't use `\\end' in internal vertical mode.\nleading text: \\end{document}\n\\begin{array} on input line 8 ended by \\end{document}.\nleading text: \\end{document}\nMissing } inserted.\nleading text: \\end{document}\nEmergency stop.\n\n<\/pre>\n<ul>\n<li> Por outro lado, a fun\u00e7\u00e3o de probabilidade cumulativa da distribui\u00e7\u00e3o de Bernoulli \u00e9 definida pela seguinte express\u00e3o:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-9e88fb8ab304bedd415fc2733481b681_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\" \\displaystyle P[X\\leq x]=\\left\\{\\begin{array}{ll}0 &amp; \\text{si } x<0\\\\[2ex]1-p&amp; \\text{si }0 \\leq x<1\\\\[2ex]1 &amp; \\text{si } x\\geq 1\\end{array}\\right.\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"269\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul>\n<li> O coeficiente de assimetria de uma distribui\u00e7\u00e3o de Bernoulli \u00e9 calculado com a seguinte express\u00e3o:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-a40989786a746b4be0d58885a7b1105c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A=\\cfrac{q-p}{\\sqrt{p\\cdot q}}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"85\" style=\"vertical-align: -18px;\"><\/p>\n<\/p>\n<ul>\n<li> Da mesma forma, a curtose de uma distribui\u00e7\u00e3o de Bernoulli depende do valor do par\u00e2metro <em>p<\/em> e pode ser encontrada aplicando a seguinte f\u00f3rmula: <\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-80241858133afe551b9687ce4131b180_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"C=\\cfrac{3p^2-3p+1}{p(1-p)}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"136\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"distribucion-de-bernoulli-y-distribucion-binomial\"><\/span> Distribui\u00e7\u00e3o de Bernoulli e distribui\u00e7\u00e3o binomial<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Nesta se\u00e7\u00e3o, veremos a diferen\u00e7a entre a distribui\u00e7\u00e3o de Bernoulli e a distribui\u00e7\u00e3o binomial, pois s\u00e3o dois tipos de distribui\u00e7\u00f5es de probabilidade relacionadas.<\/p>\n<p> A <strong>distribui\u00e7\u00e3o binomial<\/strong> conta o n\u00famero de resultados \u201cbem-sucedidos\u201d obtidos em um conjunto de testes de Bernoulli. Estas experi\u00eancias de Bernoulli devem ser independentes, mas devem ter a mesma probabilidade de sucesso.<\/p>\n<p> Portanto, <strong>a distribui\u00e7\u00e3o binomial \u00e9 a soma de um conjunto de vari\u00e1veis que segue uma distribui\u00e7\u00e3o de Bernoulli<\/strong> , todas definidas pelo mesmo par\u00e2metro <em>p<\/em> .<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-e63ec0d7ac64de1089ca7509233c30aa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}X_i\\sim \\text{Bernoulli}(p)\\\\[2ex]\\displaystyle \\sum_{i=1}^nX_i\\sim \\text{Bin}(n,p)\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"87\" width=\"140\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Portanto, na distribui\u00e7\u00e3o de Bernoulli existe apenas um experimento de Bernoulli, enquanto na distribui\u00e7\u00e3o binomial existe uma sequ\u00eancia de experimentos de Bernoulli.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Este artigo explica o que \u00e9 a distribui\u00e7\u00e3o de Bernoulli e qual \u00e9 sua f\u00f3rmula. Al\u00e9m disso, voc\u00ea encontrar\u00e1 as propriedades da distribui\u00e7\u00e3o de Bernoulli e um exerc\u00edcio resolvido para entender melhor seu significado. Qual \u00e9 a distribui\u00e7\u00e3o de Bernoulli? A distribui\u00e7\u00e3o de Bernoulli , tamb\u00e9m conhecida como distribui\u00e7\u00e3o dicot\u00f4mica , \u00e9 uma distribui\u00e7\u00e3o de [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[12],"tags":[],"class_list":["post-220","post","type-post","status-publish","format-standard","hentry","category-probabilidade"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u25b7 Distribui\u00e7\u00e3o Bernoulli<\/title>\n<meta name=\"description\" content=\"Aqui voc\u00ea encontrar\u00e1 o que \u00e9 a distribui\u00e7\u00e3o de Bernoulli, sua f\u00f3rmula, as caracter\u00edsticas da distribui\u00e7\u00e3o de Bernoulli e um exemplo concreto.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/statorials.org\/pt\/distribuicao-bernoulli\/\" \/>\n<meta property=\"og:locale\" content=\"pt_PT\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u25b7 Distribui\u00e7\u00e3o Bernoulli\" \/>\n<meta property=\"og:description\" content=\"Aqui voc\u00ea encontrar\u00e1 o que \u00e9 a distribui\u00e7\u00e3o de Bernoulli, sua f\u00f3rmula, as caracter\u00edsticas da distribui\u00e7\u00e3o de Bernoulli e um exemplo concreto.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/pt\/distribuicao-bernoulli\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-08-04T00:49:55+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-384fd7d96d4d6584739b04a6e331b251_l3.png\" \/>\n<meta name=\"author\" content=\"Dr. benjamim anderson\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Escrito por\" \/>\n\t<meta name=\"twitter:data1\" content=\"Dr. benjamim anderson\" \/>\n\t<meta name=\"twitter:label2\" content=\"Tempo estimado de leitura\" \/>\n\t<meta name=\"twitter:data2\" content=\"5 minutos\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/pt\/distribuicao-bernoulli\/\",\"url\":\"https:\/\/statorials.org\/pt\/distribuicao-bernoulli\/\",\"name\":\"\u25b7 Distribui\u00e7\u00e3o Bernoulli\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/pt\/#website\"},\"datePublished\":\"2023-08-04T00:49:55+00:00\",\"dateModified\":\"2023-08-04T00:49:55+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/pt\/#\/schema\/person\/e08f98e8db95e0aa9c310e1b27c9c666\"},\"description\":\"Aqui voc\u00ea encontrar\u00e1 o que \u00e9 a distribui\u00e7\u00e3o de Bernoulli, sua f\u00f3rmula, as caracter\u00edsticas da distribui\u00e7\u00e3o de Bernoulli e um exemplo concreto.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/pt\/distribuicao-bernoulli\/#breadcrumb\"},\"inLanguage\":\"pt-PT\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/pt\/distribuicao-bernoulli\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/pt\/distribuicao-bernoulli\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Lar\",\"item\":\"https:\/\/statorials.org\/pt\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Distribui\u00e7\u00e3o bernoulli\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/statorials.org\/pt\/#website\",\"url\":\"https:\/\/statorials.org\/pt\/\",\"name\":\"Statorials\",\"description\":\"O seu guia para a literacia estat\u00edstica!\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/statorials.org\/pt\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"pt-PT\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/statorials.org\/pt\/#\/schema\/person\/e08f98e8db95e0aa9c310e1b27c9c666\",\"name\":\"Dr. benjamim anderson\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"pt-PT\",\"@id\":\"https:\/\/statorials.org\/pt\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/statorials.org\/pt\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg\",\"contentUrl\":\"https:\/\/statorials.org\/pt\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg\",\"caption\":\"Dr. benjamim anderson\"},\"description\":\"Ol\u00e1, sou Benjamin, um professor aposentado de estat\u00edstica que se tornou professor dedicado na Statorials. Com vasta experi\u00eancia e conhecimento na \u00e1rea de estat\u00edstica, estou empenhado em compartilhar meu conhecimento para capacitar os alunos por meio de Statorials. Saber mais\",\"sameAs\":[\"https:\/\/statorials.org\/pt\"]}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"\u25b7 Distribui\u00e7\u00e3o Bernoulli","description":"Aqui voc\u00ea encontrar\u00e1 o que \u00e9 a distribui\u00e7\u00e3o de Bernoulli, sua f\u00f3rmula, as caracter\u00edsticas da distribui\u00e7\u00e3o de Bernoulli e um exemplo concreto.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/statorials.org\/pt\/distribuicao-bernoulli\/","og_locale":"pt_PT","og_type":"article","og_title":"\u25b7 Distribui\u00e7\u00e3o Bernoulli","og_description":"Aqui voc\u00ea encontrar\u00e1 o que \u00e9 a distribui\u00e7\u00e3o de Bernoulli, sua f\u00f3rmula, as caracter\u00edsticas da distribui\u00e7\u00e3o de Bernoulli e um exemplo concreto.","og_url":"https:\/\/statorials.org\/pt\/distribuicao-bernoulli\/","og_site_name":"Statorials","article_published_time":"2023-08-04T00:49:55+00:00","og_image":[{"url":"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-384fd7d96d4d6584739b04a6e331b251_l3.png"}],"author":"Dr. benjamim anderson","twitter_card":"summary_large_image","twitter_misc":{"Escrito por":"Dr. benjamim anderson","Tempo estimado de leitura":"5 minutos"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/statorials.org\/pt\/distribuicao-bernoulli\/","url":"https:\/\/statorials.org\/pt\/distribuicao-bernoulli\/","name":"\u25b7 Distribui\u00e7\u00e3o Bernoulli","isPartOf":{"@id":"https:\/\/statorials.org\/pt\/#website"},"datePublished":"2023-08-04T00:49:55+00:00","dateModified":"2023-08-04T00:49:55+00:00","author":{"@id":"https:\/\/statorials.org\/pt\/#\/schema\/person\/e08f98e8db95e0aa9c310e1b27c9c666"},"description":"Aqui voc\u00ea encontrar\u00e1 o que \u00e9 a distribui\u00e7\u00e3o de Bernoulli, sua f\u00f3rmula, as caracter\u00edsticas da distribui\u00e7\u00e3o de Bernoulli e um exemplo concreto.","breadcrumb":{"@id":"https:\/\/statorials.org\/pt\/distribuicao-bernoulli\/#breadcrumb"},"inLanguage":"pt-PT","potentialAction":[{"@type":"ReadAction","target":["https:\/\/statorials.org\/pt\/distribuicao-bernoulli\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/statorials.org\/pt\/distribuicao-bernoulli\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Lar","item":"https:\/\/statorials.org\/pt\/"},{"@type":"ListItem","position":2,"name":"Distribui\u00e7\u00e3o bernoulli"}]},{"@type":"WebSite","@id":"https:\/\/statorials.org\/pt\/#website","url":"https:\/\/statorials.org\/pt\/","name":"Statorials","description":"O seu guia para a literacia estat\u00edstica!","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/statorials.org\/pt\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"pt-PT"},{"@type":"Person","@id":"https:\/\/statorials.org\/pt\/#\/schema\/person\/e08f98e8db95e0aa9c310e1b27c9c666","name":"Dr. benjamim anderson","image":{"@type":"ImageObject","inLanguage":"pt-PT","@id":"https:\/\/statorials.org\/pt\/#\/schema\/person\/image\/","url":"https:\/\/statorials.org\/pt\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg","contentUrl":"https:\/\/statorials.org\/pt\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg","caption":"Dr. benjamim anderson"},"description":"Ol\u00e1, sou Benjamin, um professor aposentado de estat\u00edstica que se tornou professor dedicado na Statorials. Com vasta experi\u00eancia e conhecimento na \u00e1rea de estat\u00edstica, estou empenhado em compartilhar meu conhecimento para capacitar os alunos por meio de Statorials. Saber mais","sameAs":["https:\/\/statorials.org\/pt"]}]}},"yoast_meta":{"yoast_wpseo_title":"","yoast_wpseo_metadesc":"","yoast_wpseo_canonical":""},"_links":{"self":[{"href":"https:\/\/statorials.org\/pt\/wp-json\/wp\/v2\/posts\/220","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/statorials.org\/pt\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/statorials.org\/pt\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/statorials.org\/pt\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/statorials.org\/pt\/wp-json\/wp\/v2\/comments?post=220"}],"version-history":[{"count":0,"href":"https:\/\/statorials.org\/pt\/wp-json\/wp\/v2\/posts\/220\/revisions"}],"wp:attachment":[{"href":"https:\/\/statorials.org\/pt\/wp-json\/wp\/v2\/media?parent=220"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/statorials.org\/pt\/wp-json\/wp\/v2\/categories?post=220"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/statorials.org\/pt\/wp-json\/wp\/v2\/tags?post=220"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}