{"id":1021,"date":"2023-07-27T23:10:51","date_gmt":"2023-07-27T23:10:51","guid":{"rendered":"https:\/\/statorials.org\/pt\/coeficiente-multinomial\/"},"modified":"2023-07-27T23:10:51","modified_gmt":"2023-07-27T23:10:51","slug":"coeficiente-multinomial","status":"publish","type":"post","link":"https:\/\/statorials.org\/pt\/coeficiente-multinomial\/","title":{"rendered":"Coeficiente multinomial: defini\u00e7\u00e3o e exemplos"},"content":{"rendered":"

<\/p>\n

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Um coeficiente multinomial<\/strong> descreve o n\u00famero de parti\u00e7\u00f5es poss\u00edveis de n<\/em> objetos em k<\/em> grupos de tamanho n 1<\/sub><\/em> , n 2<\/sub><\/em> , \u2026, n k<\/sub><\/em> .<\/span><\/p>\n

A f\u00f3rmula para calcular um coeficiente multinomial \u00e9:<\/span><\/p>\n

Coeficiente multinomial = n! \/ (n 1<\/sub> ! * n 2<\/sub> ! * \u2026 * n k<\/sub> !)<\/span><\/p>\n

Os exemplos a seguir ilustram como calcular o coeficiente multinomial na pr\u00e1tica.<\/span><\/p>\n

Exemplo 1: letras em uma palavra<\/strong><\/span><\/h3>\n

Quantas parti\u00e7\u00f5es exclusivas da palavra ARKANSAS existem?<\/span><\/p>\n

Solu\u00e7\u00e3o:<\/strong> Podemos simplesmente inserir os seguintes valores na f\u00f3rmula do coeficiente multinomial:<\/span><\/p>\n

n<\/strong> (total de letras): 8<\/span><\/p>\n

n 1<\/sub><\/strong> (letra \u201cA\u201d): 3<\/span><\/p>\n

n 2<\/sub><\/strong> (letra \u201cR\u201d): 1<\/span><\/p>\n

n 3<\/sub><\/strong> (letra \u201cK\u201d): 1<\/span><\/p>\n

n 4<\/sub><\/strong> (letra \u201cN\u201d): 1<\/span><\/p>\n

n\u00ba 5<\/sub><\/strong> (letra \u201cS\u201d): 2<\/span><\/p>\n

Coeficiente multinomial = 8! \/ (3! * 1! * 1! * 1! * 2!) = 3,360<\/strong><\/span><\/p>\n

Existem 3.360<\/strong> parti\u00e7\u00f5es exclusivas da palavra ARKANSAS.<\/span><\/p>\n

Exemplo 2: Alunos por ano letivo<\/strong><\/span><\/h3>\n

Um grupo de seis alunos \u00e9 composto por 3 alunos do \u00faltimo ano, 2 do terceiro ano e 1 do segundo ano. Quantas pontua\u00e7\u00f5es \u00fanicas existem deste grupo de alunos por n\u00edvel?<\/span><\/p>\n

Solu\u00e7\u00e3o:<\/strong> Podemos simplesmente inserir os seguintes valores na f\u00f3rmula do coeficiente multinomial:<\/span><\/p>\n

n<\/strong> (total de alunos): 6<\/span><\/p>\n

n 1<\/sub><\/strong> (total de idosos): 3<\/span><\/p>\n

n 2<\/sub><\/strong> (total de juniores): 2<\/span><\/p>\n

n 3<\/sub><\/strong> (total de alunos do segundo ano): 1<\/span><\/p>\n

Coeficiente multinomial = 6! \/ (3! * 2! * 1!) = 60<\/strong><\/span><\/p>\n

Existem 60<\/strong> pontua\u00e7\u00f5es exclusivas desses alunos por n\u00edvel.<\/span><\/p>\n

Exemplo 3: Prefer\u00eancia partid\u00e1ria pol\u00edtica<\/strong><\/span><\/h3>\n

De um grupo de dez residentes de um determinado condado, 3 s\u00e3o republicanos, 5 democratas e 2 independentes. Quantas parti\u00e7\u00f5es \u00fanicas existem deste grupo de residentes por partido pol\u00edtico?<\/span><\/p>\n

Solu\u00e7\u00e3o:<\/strong> Podemos simplesmente inserir os seguintes valores na f\u00f3rmula do coeficiente multinomial:<\/span><\/p>\n

n<\/strong> (total de residentes): 10<\/span><\/p>\n

n\u00ba 1<\/sub><\/strong> (total de republicanos): 3<\/span><\/p>\n

N\u00ba 2<\/sub><\/strong> (total de democratas): 5<\/span><\/p>\n

n\u00ba 3<\/sub><\/strong> (total de independentes): 2<\/span><\/p>\n

Coeficiente multinomial = 10! \/ (3! * 5! * 2!) = 2,520<\/strong><\/span><\/p>\n

Existem 2.520<\/strong> reparti\u00e7\u00f5es \u00fanicas destes residentes por partido pol\u00edtico.<\/span><\/p>\n

Recursos adicionais<\/strong><\/span><\/h3>\n

O coeficiente multinomial \u00e9 usado em parte da f\u00f3rmula da distribui\u00e7\u00e3o multinomial<\/a> , que descreve a probabilidade de obter um n\u00famero espec\u00edfico de contagens para k<\/em> resultados diferentes, quando cada resultado tem uma probabilidade fixa de ocorrer.<\/span><\/p>\n

B\u00f4nus:<\/strong> voc\u00ea pode usar a Calculadora de Coeficientes Multinomiais para calcular facilmente coeficientes multinomiais.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

Um coeficiente multinomial descreve o n\u00famero de parti\u00e7\u00f5es poss\u00edveis de n objetos em k grupos de tamanho n 1 , n 2 , \u2026, n k . A f\u00f3rmula para calcular um coeficiente multinomial \u00e9: Coeficiente multinomial = n! \/ (n 1 ! * n 2 ! * \u2026 * n k !) Os exemplos […]<\/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-1021","post","type-post","status-publish","format-standard","hentry","category-guia"],"yoast_head":"\nCoeficiente multinomial: defini\u00e7\u00e3o e exemplos - Estatologia<\/title>\n<meta name=\"description\" content=\"Uma explica\u00e7\u00e3o simples de um coeficiente multinomial, incluindo uma defini\u00e7\u00e3o e v\u00e1rios exemplos.\" \/>\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\/coeficiente-multinomial\/\" \/>\n<meta property=\"og:locale\" content=\"pt_PT\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Coeficiente multinomial: defini\u00e7\u00e3o e exemplos - Estatologia\" \/>\n<meta property=\"og:description\" content=\"Uma explica\u00e7\u00e3o simples de um coeficiente multinomial, incluindo uma defini\u00e7\u00e3o e v\u00e1rios exemplos.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/pt\/coeficiente-multinomial\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-27T23:10:51+00:00\" \/>\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\/coeficiente-multinomial\/\",\"url\":\"https:\/\/statorials.org\/pt\/coeficiente-multinomial\/\",\"name\":\"Coeficiente multinomial: defini\u00e7\u00e3o e exemplos - Estatologia\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/pt\/#website\"},\"datePublished\":\"2023-07-27T23:10:51+00:00\",\"dateModified\":\"2023-07-27T23:10:51+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/pt\/#\/schema\/person\/e08f98e8db95e0aa9c310e1b27c9c666\"},\"description\":\"Uma explica\u00e7\u00e3o simples de um coeficiente multinomial, incluindo uma defini\u00e7\u00e3o e v\u00e1rios exemplos.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/pt\/coeficiente-multinomial\/#breadcrumb\"},\"inLanguage\":\"pt-PT\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/pt\/coeficiente-multinomial\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/pt\/coeficiente-multinomial\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Lar\",\"item\":\"https:\/\/statorials.org\/pt\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Coeficiente multinomial: defini\u00e7\u00e3o e exemplos\"}]},{\"@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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