{"id":831,"date":"2023-07-28T14:48:22","date_gmt":"2023-07-28T14:48:22","guid":{"rendered":"https:\/\/statorials.org\/pt\/distribuicao-binomial-python\/"},"modified":"2023-07-28T14:48:22","modified_gmt":"2023-07-28T14:48:22","slug":"distribuicao-binomial-python","status":"publish","type":"post","link":"https:\/\/statorials.org\/pt\/distribuicao-binomial-python\/","title":{"rendered":"Como usar distribui\u00e7\u00e3o binomial em python"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">A <a href=\"https:\/\/statorials.org\/pt\/distribuicao-binomial-1\/\" target=\"_blank\" rel=\"noopener\">distribui\u00e7\u00e3o binomial<\/a> \u00e9 uma das distribui\u00e7\u00f5es mais comumente usadas em estat\u00edstica. Descreve a probabilidade de obter <em>k<\/em> sucessos em <em>n<\/em> experimentos binomiais.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Se uma <a href=\"https:\/\/statorials.org\/pt\/variaveis-aleatorias\/\" target=\"_blank\" rel=\"noreferrer noopener\" aria-label=\"random variable (opens in a new tab)\">vari\u00e1vel aleat\u00f3ria<\/a> <em>X<\/em> segue uma distribui\u00e7\u00e3o binomial, ent\u00e3o a probabilidade de <em>X<\/em> = <em>k<\/em> sucesso pode ser encontrada pela seguinte f\u00f3rmula:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>P(X=k) = <sub>n<\/sub> C <sub>k<\/sub> * p <sup>k<\/sup> * (1-p) <sup>nk<\/sup><\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Ouro:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>n:<\/strong> n\u00famero de tentativas<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>k:<\/strong> n\u00famero de sucessos<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>p:<\/strong> probabilidade de sucesso em uma determinada tentativa<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong><sub>n<\/sub> C <sub>k<\/sub> :<\/strong> o n\u00famero de maneiras de obter <em>k<\/em> sucessos em <em>n<\/em> tentativas<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Este tutorial explica como usar a distribui\u00e7\u00e3o binomial em Python.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Como gerar uma distribui\u00e7\u00e3o binomial<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Voc\u00ea pode gerar uma matriz de valores que segue uma distribui\u00e7\u00e3o binomial usando a fun\u00e7\u00e3o <a href=\"https:\/\/numpy.org\/doc\/stable\/reference\/random\/generated\/numpy.random.binomial.html\" target=\"_blank\" rel=\"noopener\">random.binomial<\/a> da biblioteca numpy:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #107d3f;\">from<\/span> numpy <span style=\"color: #107d3f;\">import<\/span> random\n\n<span style=\"color: #008080;\">#generate an array of 10 values that follows a binomial distribution<\/span>\nrandom.binomial(n=10, p=.25, size=10)\n\narray([5, 2, 1, 3, 3, 3, 2, 2, 1, 4])\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">Cada n\u00famero na tabela resultante representa o n\u00famero de &#8220;sucessos&#8221; encontrados ao longo de <strong>10<\/strong> tentativas, onde a probabilidade de sucesso em uma determinada tentativa era <strong>de 0,25<\/strong> .<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Como calcular probabilidades usando uma distribui\u00e7\u00e3o binomial<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Voc\u00ea tamb\u00e9m pode responder perguntas sobre probabilidade binomial usando a <a href=\"https:\/\/docs.scipy.org\/doc\/scipy\/reference\/generated\/scipy.stats.binom.html\" target=\"_blank\" rel=\"noopener\">fun\u00e7\u00e3o binom<\/a> da biblioteca scipy.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Pergunta 1:<\/strong> Nathan acerta 60% de suas tentativas de lance livre. Se ele acertar 12 lances livres, qual \u00e9 a probabilidade de acertar exatamente 10?<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #107d3f;\">from<\/span> scipy.stats <span style=\"color: #107d3f;\">import<\/span> binom\n\n<span style=\"color: #008080;\">#calculate binomial probability<\/span>\nbinom.pmf(k= <span style=\"color: #107d3f;\">10<\/span> , n= <span style=\"color: #107d3f;\">12<\/span> , p= <span style=\"color: #107d3f;\">0.6<\/span> )\n\n0.0639\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">A probabilidade de Nathan acertar exatamente 10 lances livres \u00e9 <strong>0,0639<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Quest\u00e3o 2:<\/strong> Marty joga uma moeda honesta 5 vezes. Qual \u00e9 a probabilidade de a moeda dar cara 2 vezes ou menos?<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #107d3f;\">from<\/span> scipy.stats <span style=\"color: #107d3f;\">import<\/span> binom\n\n<span style=\"color: #008080;\">#calculate binomial probability<\/span>\nbinom.cdf(k= <span style=\"color: #107d3f;\">2<\/span> , n= <span style=\"color: #107d3f;\">5<\/span> , p= <span style=\"color: #107d3f;\">0.5<\/span> )\n\n0.5\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">A probabilidade de a moeda dar cara 2 vezes ou menos \u00e9 de <strong>0,5<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Pergunta 3:<\/strong> Sabemos que 70% dos indiv\u00edduos apoiam uma determinada lei. Se 10 indiv\u00edduos forem selecionados aleatoriamente, qual \u00e9 a probabilidade de que entre 4 e 6 deles apoiem a lei?<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #107d3f;\">from<\/span> scipy.stats <span style=\"color: #107d3f;\">import<\/span> binom\n\n<span style=\"color: #008080;\">#calculate binomial probability<\/span>\nbinom.cdf(k= <span style=\"color: #107d3f;\">6<\/span> , n= <span style=\"color: #107d3f;\">10<\/span> , p= <span style=\"color: #107d3f;\">0.7<\/span> ) - binom.cdf(k= <span style=\"color: #107d3f;\">3<\/span> , n= <span style=\"color: #107d3f;\">10<\/span> , p= <span style=\"color: #107d3f;\">0.7<\/span> )\n\n0.3398\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">A probabilidade de que entre 4 e 6 indiv\u00edduos selecionados aleatoriamente apoiem a lei \u00e9 de <strong>0,3398<\/strong> .<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Como visualizar uma distribui\u00e7\u00e3o binomial<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Voc\u00ea pode visualizar uma distribui\u00e7\u00e3o binomial em Python usando as bibliotecas <strong>seaborn<\/strong> e <strong>matplotlib<\/strong> :<\/span> <\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #107d3f;\">from<\/span> numpy <span style=\"color: #107d3f;\">import<\/span> random\n<span style=\"color: #107d3f;\">import<\/span> matplotlib.pyplot <span style=\"color: #107d3f;\">as<\/span> plt\n<span style=\"color: #107d3f;\">import<\/span> seaborn <span style=\"color: #107d3f;\">as<\/span> sns\n\nx = random.binomial(n= <span style=\"color: #107d3f;\">10<\/span> , p= <span style=\"color: #107d3f;\">0.5<\/span> , size= <span style=\"color: #107d3f;\">1000<\/span> )\n\nsns.distplot(x, hist= <span style=\"color: #107d3f;\">True<\/span> , kde= <span style=\"color: #107d3f;\">False<\/span> )\n\nplt.show()\n<\/strong><\/pre>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-9215 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/binomepython1.png\" alt=\"Gr\u00e1fico de distribui\u00e7\u00e3o binomial em Python\" width=\"396\" height=\"262\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Ch\u00e1<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>A distribui\u00e7\u00e3o binomial \u00e9 uma das distribui\u00e7\u00f5es mais comumente usadas em estat\u00edstica. Descreve a probabilidade de obter k sucessos em n experimentos binomiais. Se uma vari\u00e1vel aleat\u00f3ria X segue uma distribui\u00e7\u00e3o binomial, ent\u00e3o a probabilidade de X = k sucesso pode ser encontrada pela seguinte f\u00f3rmula: P(X=k) = n C k * p k * [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[11],"tags":[],"class_list":["post-831","post","type-post","status-publish","format-standard","hentry","category-guia"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Como usar a distribui\u00e7\u00e3o binomial em Python - Estatologia<\/title>\n<meta name=\"description\" content=\"Uma explica\u00e7\u00e3o simples sobre como usar a distribui\u00e7\u00e3o binomial em Python.\" \/>\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-binomial-python\/\" \/>\n<meta property=\"og:locale\" content=\"pt_PT\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Como usar a distribui\u00e7\u00e3o binomial em Python - Estatologia\" \/>\n<meta property=\"og:description\" content=\"Uma explica\u00e7\u00e3o simples sobre como usar a distribui\u00e7\u00e3o binomial em Python.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/pt\/distribuicao-binomial-python\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-28T14:48:22+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/binomepython1.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=\"2 minutos\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/pt\/distribuicao-binomial-python\/\",\"url\":\"https:\/\/statorials.org\/pt\/distribuicao-binomial-python\/\",\"name\":\"Como usar a distribui\u00e7\u00e3o binomial em Python - Estatologia\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/pt\/#website\"},\"datePublished\":\"2023-07-28T14:48:22+00:00\",\"dateModified\":\"2023-07-28T14:48:22+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/pt\/#\/schema\/person\/e08f98e8db95e0aa9c310e1b27c9c666\"},\"description\":\"Uma explica\u00e7\u00e3o simples sobre como usar a distribui\u00e7\u00e3o binomial em Python.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/pt\/distribuicao-binomial-python\/#breadcrumb\"},\"inLanguage\":\"pt-PT\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/pt\/distribuicao-binomial-python\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/pt\/distribuicao-binomial-python\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Lar\",\"item\":\"https:\/\/statorials.org\/pt\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Como usar distribui\u00e7\u00e3o binomial em python\"}]},{\"@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. 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