{"id":910703,"date":"2021-11-28T18:49:00","date_gmt":"2021-11-28T21:49:00","guid":{"rendered":"https:\/\/www.estrategiaconcursos.com.br\/blog\/?p=910703"},"modified":"2021-11-22T14:27:14","modified_gmt":"2021-11-22T17:27:14","slug":"variaveis-aleatorias-continuas-iss-bh-estatistica","status":"publish","type":"post","link":"https:\/\/www.estrategiaconcursos.com.br\/blog\/variaveis-aleatorias-continuas-iss-bh-estatistica\/","title":{"rendered":"Resumo das Vari\u00e1veis Aleat\u00f3rias Cont\u00ednuas ISS-BH \u2013 Estat\u00edstica"},"content":{"rendered":"\n<p>Ol\u00e1, pessoal. Tudo certo? No artigo de hoje veremos o Resumo das Vari\u00e1veis Aleat\u00f3rias Cont\u00ednuas ISS-BH.<\/p>\n\n\n\n<p>T\u00f3picos que ser\u00e3o vistos:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>Conceitos Gerais<\/li><li>Fun\u00e7\u00e3o de distribui\u00e7\u00e3o acumulada<\/li><li>Distribui\u00e7\u00e3o Uniforme<\/li><li>Distribui\u00e7\u00e3o exponencial<\/li><li>Distribui\u00e7\u00e3o normal<\/li><\/ul>\n\n\n\n<p>Preparado (a)? Vamos l\u00e1.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Conceitos Gerais<\/h2>\n\n\n\n<p>Iniciemos o Resumo das Vari\u00e1veis Aleat\u00f3rias Cont\u00ednuas ISS-BH pelos conceitos gerais\/iniciais.<\/p>\n\n\n\n<p><strong><span class=\"has-inline-color has-vivid-cyan-blue-color\">Vari\u00e1veis <\/span><\/strong><span class=\"has-inline-color has-vivid-cyan-blue-color\"><strong>aleat\u00f3rias cont\u00ednuas<\/strong> <\/span>s\u00e3o aquelas que podem assumir quaisquer valores dentro de um intervalo, assim podemos dizer que elas n\u00e3o podem ser enumeradas (contadas), como por exemplo, a altura.<\/p>\n\n\n\n<p>Nesse caso da altura, uma pessoa pode ter 1,80m de altura, entretanto se melhorar a precis\u00e3o poderia ser 1,802m, ou seja, a probabilidade de um valor espec\u00edfico dentro de um intervalo \u00e9 nula.<\/p>\n\n\n\n<p>Assim, ao inv\u00e9s de utilizarmos uma fun\u00e7\u00e3o de probabilidade f (x) = P (X = x) como nas vari\u00e1veis discretas, utilizamos uma <strong>fun\u00e7\u00e3o densidade de probabilidade<\/strong> (f.d.p), para trabalhar com intervalos.<\/p>\n\n\n\n<p><strong><span class=\"has-inline-color has-vivid-green-cyan-color\">Condi\u00e7\u00f5es da fun\u00e7\u00e3o densidade de probabilidade:<\/span><\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>Uma probabilidade qualquer nunca \u00e9 negativa<\/li><li>A probabilidade associada a todo o Espa\u00e7o Amostral \u00e9 igual a 100%<\/li><\/ul>\n\n\n\n<p>Nesse sentido, a <strong>probabilidade<\/strong> ser\u00e1 dada pela <strong>\u00e1rea da fun\u00e7\u00e3o<\/strong>.<\/p>\n\n\n\n<p><strong><span class=\"has-inline-color has-vivid-green-cyan-color\">Exemplo<\/span>: <\/strong>(VUNESP\/2014 \u2013 TJ-PA) Uma vari\u00e1vel aleat\u00f3ria cont\u00ednua tem uma fun\u00e7\u00e3o de probabilidade dada por f(x) = K.x, v\u00e1lida apenas no intervalo 1\u2264 x \u2264 2. Fora desse intervalo f(x) = 0. De acordo com isso o valor de K \u00e9:<\/p>\n\n\n\n<p>Integral de k.x dx \u00e9 igual a<\/p>\n\n\n\n<p>&nbsp;(k\/2) .&nbsp; x\u00b2 = 1<\/p>\n\n\n\n<p>Tendo como intervalo de 2 e 1, assim &nbsp;<\/p>\n\n\n\n<p>k\/2 . (2\u00b2 &#8211; 1\u00b2) = 1<\/p>\n\n\n\n<p>Logo,<\/p>\n\n\n\n<p>k\/2 . 3 = 1<\/p>\n\n\n\n<p>Assim,<\/p>\n\n\n\n<p>K = 2\/3<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Fun\u00e7\u00e3o de distribui\u00e7\u00e3o acumulada<\/h2>\n\n\n\n<p>A <strong><span class=\"has-inline-color has-vivid-cyan-blue-color\">fun\u00e7\u00e3o de distribui\u00e7\u00e3o acumulada<\/span><\/strong> basicamente \u00e9 a probabilidade acumulada desde o in\u00edcio at\u00e9 o ponto indicado.<\/p>\n\n\n\n<p>Vamos ver por meio de um exemplo, mas antes disso vejamos as caracter\u00edsticas da fun\u00e7\u00e3o acumulada.<\/p>\n\n\n\n<p><strong><span class=\"has-inline-color has-vivid-green-cyan-color\">Caracter\u00edsticas<\/span><\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>FA \u00e9 n\u00e3o decrescente, pois as probabilidades s\u00e3o sempre somadas.<\/li><li>Por ser uma probabilidade, a f.d.a. assume valores entre 0 e 1<\/li><\/ul>\n\n\n\n<p><strong><span class=\"has-inline-color has-vivid-green-cyan-color\">Exemplo<\/span><\/strong>: (FCC\/2012 \u2013 Analista Judici\u00e1rio do TRF da 2\u00aa Regi\u00e3o) Uma vari\u00e1vel aleat\u00f3ria cont\u00ednua tem fun\u00e7\u00e3o densidade de probabilidade dada por:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/11\/17154158\/image-360.png\" alt=\"\" class=\"wp-image-910705\" width=\"220\" height=\"93\"\/><figcaption> Exerc\u00edcio &#8211; Fun\u00e7\u00e3o de distribui\u00e7\u00e3o acumulada <\/figcaption><\/figure><\/div>\n\n\n\n<p>Se F(x) \u00e9 a fun\u00e7\u00e3o de distribui\u00e7\u00e3o de X, ent\u00e3o F(2) \u00e9 igual a:<\/p>\n\n\n\n<p>Primeiro deve-se integrar 2\/x\u00b3,<\/p>\n\n\n\n<p>= 2 . x^-2 \/ -2<\/p>\n\n\n\n<p>= -x^-2<\/p>\n\n\n\n<p>= -1\/x\u00b2<\/p>\n\n\n\n<p>E adotando os limites de 1 (limite inferior) at\u00e9 o ponto desejado (2).<\/p>\n\n\n\n<p>F(2) = (-1\/2\u00b2) \u2013 (-1\/1\u00b2)<\/p>\n\n\n\n<p>F(2) = -1\/4 + 1<\/p>\n\n\n\n<p>F(2) = 3\/4<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Medidas de posi\u00e7\u00e3o central<\/h3>\n\n\n\n<p>Sabemos que a <span class=\"has-inline-color has-vivid-green-cyan-color\"><strong>mediana<\/strong> <\/span>divide em duas partes iguais a distribui\u00e7\u00e3o, assim devemos igualar a f.d.p em 50%<\/p>\n\n\n\n<p><strong><span class=\"has-inline-color has-vivid-purple-color\">Exemplo<\/span>:<\/strong> F(x) = 8x\u00b2<\/p>\n\n\n\n<p>8x\u00b2 = 1\/2<\/p>\n\n\n\n<p>x\u00b2 = 1\/16<\/p>\n\n\n\n<p>x = sqrt (1\/16)<\/p>\n\n\n\n<p>x = 1\/4<\/p>\n\n\n\n<p>A <span class=\"has-inline-color has-vivid-green-cyan-color\"><strong>moda<\/strong> <\/span>\u00e9 o valor correspondente a maior frequ\u00eancia\/probabilidade.<\/p>\n\n\n\n<p>\u00c9 poss\u00edvel verificar graficamente, mas na impossibilidade temos que derivar a fun\u00e7\u00e3o.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"369\" height=\"83\" src=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/11\/17154215\/image-361.png\" alt=\"\" class=\"wp-image-910707\" srcset=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/11\/17154215\/image-361.png 369w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/11\/17154215\/image-361-300x67.png 300w\" sizes=\"auto, (max-width: 369px) 100vw, 369px\" \/><figcaption>Moda &#8211; Fun\u00e7\u00e3o de distribui\u00e7\u00e3o acumulada<\/figcaption><\/figure><\/div>\n\n\n\n<p><strong><span class=\"has-inline-color has-vivid-green-cyan-color\">Exemplo<\/span>:<\/strong> (FCC\/2011 \u2013 Analista Judici\u00e1rio do TRT da 1\u00aa Regi\u00e3o) Considere a vari\u00e1vel aleat\u00f3ria cont\u00ednua X com fun\u00e7\u00e3o densidade de probabilidade dada por:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"303\" height=\"97\" src=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/11\/17154226\/image-362.png\" alt=\"\" class=\"wp-image-910708\" srcset=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/11\/17154226\/image-362.png 303w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/11\/17154226\/image-362-300x96.png 300w\" sizes=\"auto, (max-width: 303px) 100vw, 303px\" \/><figcaption>Exerc\u00edcio &#8211; Fun\u00e7\u00e3o de distribui\u00e7\u00e3o acumulada<\/figcaption><\/figure><\/div>\n\n\n\n<p>Valor da moda ser\u00e1:<\/p>\n\n\n\n<p>f (x) = 12x\u00b2 &#8211; 12x\u00b3<\/p>\n\n\n\n<p>Derivando a fun\u00e7\u00e3o<\/p>\n\n\n\n<p>12 . 2 x\u00b9 &#8211; 12 . 3x\u00b2<\/p>\n\n\n\n<p>24x \u2013 36x\u00b2<\/p>\n\n\n\n<p>Igualando a 0<\/p>\n\n\n\n<p>24x \u2013 36x\u00b2 = 0<\/p>\n\n\n\n<p>Agora podemos simplificar por \/12x<\/p>\n\n\n\n<p>2 \u2013 3x = 0<\/p>\n\n\n\n<p>Logo, a moda ser\u00e1:<\/p>\n\n\n\n<p>x = 2\/3<\/p>\n\n\n\n<p>Tanto a m\u00e9dia quanto a vari\u00e2ncia podemos calcular a partir das integrais.<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li><strong><span class=\"has-inline-color has-vivid-green-cyan-color\">Esperan\u00e7a Matem\u00e1tica<\/span><\/strong><\/li><\/ul>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"339\" height=\"62\" src=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/11\/17154239\/image-363.png\" alt=\"\" class=\"wp-image-910710\" srcset=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/11\/17154239\/image-363.png 339w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/11\/17154239\/image-363-300x55.png 300w\" sizes=\"auto, (max-width: 339px) 100vw, 339px\" \/><figcaption>Esperan\u00e7a &#8211; Fun\u00e7\u00e3o de distribui\u00e7\u00e3o acumulada<\/figcaption><\/figure><\/div>\n\n\n\n<ul class=\"wp-block-list\"><li><strong><span class=\"has-inline-color has-vivid-green-cyan-color\">Vari\u00e2ncia<\/span><\/strong><\/li><\/ul>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"373\" height=\"64\" src=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/11\/17154248\/image-364.png\" alt=\"Vari\u00e1veis Aleat\u00f3rias Cont\u00ednuas ISS-BH\" class=\"wp-image-910711\" srcset=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/11\/17154248\/image-364.png 373w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/11\/17154248\/image-364-300x51.png 300w\" sizes=\"auto, (max-width: 373px) 100vw, 373px\" \/><figcaption>Vari\u00e2ncia &#8211; Fun\u00e7\u00e3o de distribui\u00e7\u00e3o acumulada<\/figcaption><\/figure><\/div>\n\n\n\n<h2 class=\"wp-block-heading\">Distribui\u00e7\u00e3o Uniforme<\/h2>\n\n\n\n<p>Dando continuidade ao Resumo das Vari\u00e1veis Aleat\u00f3rias Cont\u00ednuas ISS-BH, vejamos sobre a Distribui\u00e7\u00e3o uniforme.<\/p>\n\n\n\n<p>A <strong><span class=\"has-inline-color has-vivid-cyan-blue-color\">Distribui\u00e7\u00e3o uniforme<\/span><\/strong> apresenta o mesmo valor de probabilidade para qualquer valor.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"403\" height=\"132\" src=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/11\/17154255\/image-365.png\" alt=\"Vari\u00e1veis Aleat\u00f3rias Cont\u00ednuas ISS-BH\" class=\"wp-image-910712\" srcset=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/11\/17154255\/image-365.png 403w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/11\/17154255\/image-365-300x98.png 300w\" sizes=\"auto, (max-width: 403px) 100vw, 403px\" \/><figcaption>Distribui\u00e7\u00e3o Uniforme<\/figcaption><\/figure><\/div>\n\n\n\n<p>Assim, para calcular um intervalo em uma distribui\u00e7\u00e3o uniforme basta calcular a \u00e1rea do per\u00edodo desejado.<\/p>\n\n\n\n<p><strong><span class=\"has-inline-color has-vivid-green-cyan-color\">Exemplo:<\/span><\/strong> (FGV\/2017 \u2013 IBGE) Uma vari\u00e1vel aleat\u00f3ria cont\u00ednua X \u00e9 uniformemente distribu\u00edda no intervalo real [0, 50]. A probabilidade de que X seja maior do que 20 \u00e9 igual a:<\/p>\n\n\n\n<p>K x (50 \u2013 0) = 1<\/p>\n\n\n\n<p>K x 50 = 1<\/p>\n\n\n\n<p>K = 1\/50<\/p>\n\n\n\n<p>Para a \u00e1rea desejada<\/p>\n\n\n\n<p>P = (50 \u2013 20) x 1\/50<\/p>\n\n\n\n<p>P = 30 x 1\/50<\/p>\n\n\n\n<p>P = 0,6<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li><strong><span class=\"has-inline-color has-vivid-green-cyan-color\">Esperan\u00e7a Matem\u00e1tica<\/span><\/strong><\/li><\/ul>\n\n\n\n<p>Como estamos falando de um ret\u00e2ngulo, o valor da m\u00e9dia ser\u00e1 exatamente no meio<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"567\" height=\"221\" src=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/11\/17154305\/image-366.png\" alt=\"Vari\u00e1veis Aleat\u00f3rias Cont\u00ednuas ISS-BH\" class=\"wp-image-910714\" srcset=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/11\/17154305\/image-366.png 567w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/11\/17154305\/image-366-300x117.png 300w\" sizes=\"auto, (max-width: 567px) 100vw, 567px\" \/><figcaption>Esperan\u00e7a &#8211; Distribui\u00e7\u00e3o Uniforme<\/figcaption><\/figure><\/div>\n\n\n\n<ul class=\"wp-block-list\"><li><strong><span class=\"has-inline-color has-vivid-green-cyan-color\">Vari\u00e2ncia<\/span><\/strong><\/li><\/ul>\n\n\n\n<p>J\u00e1 a vari\u00e2ncia temos:<\/p>\n\n\n\n<p>V (X) = (b \u2013 a)\u00b2 \/ 12<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Distribui\u00e7\u00e3o exponencial<\/h2>\n\n\n\n<p>A <strong><span class=\"has-inline-color has-vivid-cyan-blue-color\">distribui\u00e7\u00e3o exponencial<\/span><\/strong> taxa de falha constante e comporta-se, como o nome sugere, de forma exponencial.<\/p>\n\n\n\n<p>Fun\u00e7\u00e3o densidade de probabilidade (f.d.p.)<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"459\" height=\"98\" src=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/11\/17154314\/image-367.png\" alt=\"Vari\u00e1veis Aleat\u00f3rias Cont\u00ednuas ISS-BH\" class=\"wp-image-910716\" srcset=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/11\/17154314\/image-367.png 459w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/11\/17154314\/image-367-300x64.png 300w\" sizes=\"auto, (max-width: 459px) 100vw, 459px\" \/><figcaption>Distribui\u00e7\u00e3o exponencial<\/figcaption><\/figure><\/div>\n\n\n\n<p>Ainda, podemos calcular a probabilidade para um X maior do que algum valor, ou em outros termos, a <strong>fun\u00e7\u00e3o de distribui\u00e7\u00e3o acumulada<\/strong> no ponto.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"243\" height=\"51\" src=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/11\/17154321\/image-368.png\" alt=\"\" class=\"wp-image-910718\"\/><\/figure><\/div>\n\n\n\n<ul class=\"wp-block-list\"><li><strong><span class=\"has-inline-color has-vivid-green-cyan-color\">Esperan\u00e7a matem\u00e1tica<\/span><\/strong><\/li><\/ul>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"155\" height=\"60\" src=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/11\/17154327\/image-369.png\" alt=\"\" class=\"wp-image-910719\"\/><\/figure><\/div>\n\n\n\n<ul class=\"wp-block-list\"><li><strong><span class=\"has-inline-color has-vivid-green-cyan-color\">Vari\u00e2ncia<\/span><\/strong><\/li><\/ul>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"157\" height=\"62\" src=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/11\/17154333\/image-370.png\" alt=\"Vari\u00e1veis Aleat\u00f3rias Cont\u00ednuas ISS-BH\" class=\"wp-image-910720\"\/><\/figure><\/div>\n\n\n\n<p><strong><span class=\"has-inline-color has-vivid-green-cyan-color\">Exemplo<\/span>:<\/strong> FGV &#8211; Analista Judici\u00e1rio (TJ AL)\/Apoio Especializado\/Estat\u00edstica\/2018&nbsp;<\/p>\n\n\n\n<p>Suponha que o tempo de espera para a marca\u00e7\u00e3o de uma 1\u00aa audi\u00eancia nas varas de fam\u00edlia de um tribunal seja uma vari\u00e1vel aleat\u00f3ria que depende do n\u00famero de novas a\u00e7\u00f5es, seguindo uma distribui\u00e7\u00e3o exponencial com m\u00e9dia de 2,5 meses.<\/p>\n\n\n\n<p>Ent\u00e3o, trabalhando com&nbsp; e^\u22120,4 = 2\/3 , probabilidade de que uma 1\u00aa audi\u00eancia seja marcada para mais do que 2 meses depois \u00e9 igual a aproximadamente:<\/p>\n\n\n\n<p>F(2) = 1 &#8211; (2\/3)\u00b2<\/p>\n\n\n\n<p>F(2) = 1 &#8211; 4\/9<\/p>\n\n\n\n<p>F(2) = 5\/9<\/p>\n\n\n\n<p>Assim, a chance de ser marcada at\u00e9 2 meses \u00e9 de 5\/9<\/p>\n\n\n\n<p>Ent\u00e3o a chance para depois de 2 meses ser\u00e1 o complemento<\/p>\n\n\n\n<p>P = 1 &#8211; 5\/9<\/p>\n\n\n\n<p><strong>P = 4\/9<\/strong><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Distribui\u00e7\u00e3o Normal<\/h2>\n\n\n\n<p>Para finalizar o Resumo das Vari\u00e1veis Aleat\u00f3rias Cont\u00ednuas ISS-BH, vamos revisar a Distribui\u00e7\u00e3o Normal.<\/p>\n\n\n\n<p>A <strong><span class=\"has-inline-color has-vivid-cyan-blue-color\">Distribui\u00e7\u00e3o normal<\/span><\/strong> (gaussiana) \u00e9 a distribui\u00e7\u00e3o mais cobrada entre as cont\u00ednuas, ent\u00e3o \u00e9 necess\u00e1rio uma aten\u00e7\u00e3o redobrada.<\/p>\n\n\n\n<p>A distribui\u00e7\u00e3o pode ser demonstrada graficamente:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"567\" height=\"327\" src=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/11\/17154354\/image-371.png\" alt=\"Vari\u00e1veis Aleat\u00f3rias Cont\u00ednuas ISS-BH\" class=\"wp-image-910722\" srcset=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/11\/17154354\/image-371.png 567w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/11\/17154354\/image-371-300x173.png 300w\" sizes=\"auto, (max-width: 567px) 100vw, 567px\" \/><figcaption> Distribui\u00e7\u00e3o Normal <\/figcaption><\/figure><\/div>\n\n\n\n<p>Para que possamos encontrar o valor da probabilidade devemos consultar em uma tabela (a maioria dos exerc\u00edcios fornece por meio de dados), entretanto antes devemos transformar os valores do exerc\u00edcio para valores normalizados.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"136\" height=\"56\" src=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/11\/17154411\/image-372.png\" alt=\"Vari\u00e1veis Aleat\u00f3rias Cont\u00ednuas ISS-BH\" class=\"wp-image-910724\"\/><figcaption> Transforma\u00e7\u00e3o &#8211; Distribui\u00e7\u00e3o Normal <\/figcaption><\/figure><\/div>\n\n\n\n<p><strong><span class=\"has-inline-color has-vivid-green-cyan-color\">Exemplo:&nbsp;<\/span><\/strong>(FGV\/2016 \u2013 IBGE) Sabe-se que as notas de uma prova t\u00eam distribui\u00e7\u00e3o Normal com m\u00e9dia = 6,5 e vari\u00e2ncia = 4 . Adicionalmente, s\u00e3o conhecidos alguns valores tabulados da normal-padr\u00e3o.<\/p>\n\n\n\n<p>Z(1,3 ) \u2245 0,90; &nbsp;Z(1,65) \u2245 0,95; Z(1,95 ) \u2245 0,975; Onde, Z \u00e9 a fun\u00e7\u00e3o distribui\u00e7\u00e3o acumulada da<\/p>\n\n\n\n<p>Normal Padr\u00e3o.<\/p>\n\n\n\n<p>Considerando-se que apenas os 10% que atinjam as maiores notas ser\u00e3o aprovados, a nota m\u00ednima para aprova\u00e7\u00e3o \u00e9:<\/p>\n\n\n\n<p>1,3 = x \u2013 6,5 \/ sqrt 4<\/p>\n\n\n\n<p>1,3 . 2 = x \u2013 6,5<\/p>\n\n\n\n<p>X = 9,1<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Considera\u00e7\u00f5es Finais<\/h2>\n\n\n\n<p>Pessoal, chegamos ao final do Resumo das Vari\u00e1veis Aleat\u00f3rias Cont\u00ednuas ISS-BH. Espero que o artigo tenha sido efetivo para seu aprendizado.<\/p>\n\n\n\n<p>Obviamente trata-se de um resumo apenas com os pontos principais da mat\u00e9ria, tendo outros temas correlacionados como a <strong>Desigualdade de Chebyshev, Distribui\u00e7\u00e3o t-Student <\/strong>entre outros, assim n\u00e3o deixe de acompanhar as aulas para o aprofundamento necess\u00e1rio.<\/p>\n\n\n\n<p>Ainda, ressaltamos mais uma vez a import\u00e2ncia de praticar por exerc\u00edcios, assim fa\u00e7a muitas quest\u00f5es pelo nosso sistema de quest\u00f5es.<\/p>\n\n\n\n<p class=\"has-text-align-center\"><a href=\"https:\/\/concursos.estrategiaeducacional.com.br\/\">Sistema de Quest\u00f5es (SQ) \u2013 Estrat\u00e9gia Concursos<\/a><\/p>\n\n\n\n<p>Gostou do artigo? 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Tudo certo? No artigo de hoje veremos o Resumo das Vari\u00e1veis Aleat\u00f3rias Cont\u00ednuas ISS-BH. T\u00f3picos que ser\u00e3o vistos: Conceitos Gerais Fun\u00e7\u00e3o de distribui\u00e7\u00e3o acumulada Distribui\u00e7\u00e3o Uniforme Distribui\u00e7\u00e3o exponencial Distribui\u00e7\u00e3o normal Preparado (a)? Vamos l\u00e1. Conceitos Gerais Iniciemos o Resumo das Vari\u00e1veis Aleat\u00f3rias Cont\u00ednuas ISS-BH pelos conceitos gerais\/iniciais. Vari\u00e1veis aleat\u00f3rias cont\u00ednuas s\u00e3o aquelas que [&hellip;]<\/p>\n","protected":false},"author":1763,"featured_media":900232,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"post_tipo":"article","footnotes":""},"categories":[1,220183],"tags":[],"tax_estado":[219974],"class_list":["post-910703","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-cursos-e-concursos","category-fiscal-municipal","tax_estado-mg"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v27.2 (Yoast SEO v27.2) - https:\/\/yoast.com\/product\/yoast-seo-premium-wordpress\/ -->\n<title>Resumo das Vari\u00e1veis Aleat\u00f3rias Cont\u00ednuas ISS-BH \u2013 Estat\u00edstica<\/title>\n<meta name=\"description\" content=\"Veja neste artigo o Resumo das Vari\u00e1veis Aleat\u00f3rias Cont\u00ednuas ISS-BH, tais como distribui\u00e7\u00e3o acumulada, uniforme, exponencial e 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