{"id":3936,"date":"2023-07-14T16:01:08","date_gmt":"2023-07-14T16:01:08","guid":{"rendered":"https:\/\/statorials.org\/pt\/valor-esperado-x3\/"},"modified":"2023-07-14T16:01:08","modified_gmt":"2023-07-14T16:01:08","slug":"valor-esperado-x3","status":"publish","type":"post","link":"https:\/\/statorials.org\/pt\/valor-esperado-x3\/","title":{"rendered":"Como calcular o valor esperado de x^3"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">Para uma <a href=\"https:\/\/statorials.org\/pt\/variaveis-aleatorias\/\" target=\"_blank\" rel=\"noopener\">vari\u00e1vel aleat\u00f3ria<\/a> , denotada por X, voc\u00ea pode usar a seguinte f\u00f3rmula para calcular o valor esperado de X <sup>3<\/sup> :<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>E(X <sup>3<\/sup> ) = \u03a3x <sup>3<\/sup> * p(x)<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Ouro:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>\u03a3<\/strong> : Um s\u00edmbolo que significa \u201csoma\u201d<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>x<\/strong> : O valor da vari\u00e1vel aleat\u00f3ria<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>p (x)<\/strong> : A probabilidade de a vari\u00e1vel aleat\u00f3ria assumir um determinado valor<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">O exemplo a seguir mostra como usar esta f\u00f3rmula na pr\u00e1tica.<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>Exemplo: C\u00e1lculo do valor esperado de X <sup>3<\/sup><\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">Suponha que temos a seguinte tabela de distribui\u00e7\u00e3o de probabilidade que descreve a probabilidade de uma vari\u00e1vel aleat\u00f3ria,<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-31621 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/x2_1.jpg\" alt=\"\" width=\"266\" height=\"253\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Para calcular o valor esperado de X <sup>3<\/sup> , podemos usar a seguinte f\u00f3rmula:<\/span><\/p>\n<p> <span style=\"color: #000000;\">E(X <sup>3<\/sup> ) = \u03a3x <sup>3<\/sup> * p(x)<\/span><\/p>\n<p> <span style=\"color: #000000;\">E (X <sup>3<\/sup> ) = (0) <sup>3<\/sup> * 0,06 + (1) <sup>3<\/sup> * 0,15 + (2) <sup>3<\/sup> * 0,17 + (3) <sup>3<\/sup> * 0,24 + (4) <sup>3<\/sup> * 0,23 + (5) <sup>3<\/sup> *0,09 + (6) <sup>3<\/sup> *0,06<\/span><\/p>\n<p> <span style=\"color: #000000;\">E( <sup>X3<\/sup> ) = 0 + 0,15 + 0,1,36 + 6,48 + 14,72 + 11,25 + 12,96<\/span><\/p>\n<p> <span style=\"color: #000000;\">E( <sup>X3<\/sup> ) = 45,596<\/span><\/p>\n<p> <span style=\"color: #000000;\">O valor esperado de X <sup>3<\/sup> \u00e9 <strong>45.596<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Observe que esta vari\u00e1vel aleat\u00f3ria \u00e9 uma <strong>vari\u00e1vel aleat\u00f3ria discreta<\/strong> , o que significa que s\u00f3 pode assumir um n\u00famero finito de valores.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Se X for uma <strong>vari\u00e1vel aleat\u00f3ria cont\u00ednua<\/strong> , devemos usar a seguinte f\u00f3rmula para calcular o valor esperado de X <sup>3<\/sup> :<\/span><\/p>\n<p> <strong><span style=\"color: #000000;\">E(X <sup>3<\/sup> ) = \u222b x <sup>3<\/sup> f(x)dx<\/span><\/strong><\/p>\n<p> <span style=\"color: #000000;\">Ouro:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">\u222b: Um s\u00edmbolo que significa \u201cintegra\u00e7\u00e3o\u201d<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>f(x)<\/strong> : O <a href=\"https:\/\/statorials.org\/pt\/cdf-x-pdf\/\" target=\"_blank\" rel=\"noopener\">pdf<\/a> continua para a vari\u00e1vel aleat\u00f3ria<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Ao calcular o valor esperado <sup>de<\/sup><\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>Recursos adicionais<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">Os tutoriais a seguir explicam como realizar outras tarefas comuns em estat\u00edstica:<\/span><\/p>\n<p> <a href=\"https:\/\/statorials.org\/pt\/media-da-distribuicao-de-probabilidade\/\" target=\"_blank\" rel=\"noopener\">Como encontrar a m\u00e9dia de uma distribui\u00e7\u00e3o de probabilidade<\/a><br \/> <a href=\"https:\/\/statorials.org\/pt\/desvio-padrao-da-distribuicao-de-probabilidade\/\" target=\"_blank\" rel=\"noopener\">Como encontrar o desvio padr\u00e3o de uma distribui\u00e7\u00e3o de probabilidade<\/a><br \/> <a href=\"https:\/\/statorials.org\/pt\/variancia-da-distribuicao-de-probabilidade\/\" target=\"_blank\" rel=\"noopener\">Como encontrar a vari\u00e2ncia de uma distribui\u00e7\u00e3o de probabilidade<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Para uma vari\u00e1vel aleat\u00f3ria , denotada por X, voc\u00ea pode usar a seguinte f\u00f3rmula para calcular o valor esperado de X 3 : E(X 3 ) = \u03a3x 3 * p(x) Ouro: \u03a3 : Um s\u00edmbolo que significa \u201csoma\u201d x : O valor da vari\u00e1vel aleat\u00f3ria p (x) : A probabilidade de a vari\u00e1vel aleat\u00f3ria [&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-3936","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 calcular o valor esperado de X^3 - Estatologia<\/title>\n<meta name=\"description\" content=\"Este tutorial explica como calcular o valor esperado de X^3, com um exemplo.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" 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