{"id":751231,"date":"2021-05-25T21:19:13","date_gmt":"2021-05-26T00:19:13","guid":{"rendered":"https:\/\/www.estrategiaconcursos.com.br\/blog\/?p=751231"},"modified":"2021-05-25T21:30:41","modified_gmt":"2021-05-26T00:30:41","slug":"recurso-de-estatistica-para-prova-pf","status":"publish","type":"post","link":"https:\/\/www.estrategiaconcursos.com.br\/blog\/recurso-de-estatistica-para-prova-pf\/","title":{"rendered":"Recurso de Estat\u00edstica para Prova PF"},"content":{"rendered":"\n<p>Oi pessoal! Tudo bem? O gabarito preliminar da PF saiu h\u00e1 pouco e acreditamos que existe possibilidade de recurso para uma quest\u00e3o. \u00c9 a quest\u00e3o do bloco 40 &#8211; 42 que trata da esperan\u00e7a condicionada.<\/p>\n\n\n\n<p>Aqui, vou resolver a quest\u00e3o de forma mais t\u00e9cnica e direta, utilizando 2 formas de resolu\u00e7\u00e3o diferentes, no intuito de facilitar o trabalho daqueles que pretendem interpor recurso. Se preferir um passo a passo mais detalhado, d\u00e1 uma olhadinha neste <a href=\"https:\/\/www.estrategiaconcursos.com.br\/blog\/gabarito-pf-estatistica-agente-escrivao-e-papiloscopista\/\">artigo<\/a> que publicamos no dia da prova da PF com a resolu\u00e7\u00e3o detalhada de todas as quest\u00f5es de Estat\u00edstica.<\/p>\n\n\n\n<p><strong>Considere que X e Y sejam vari\u00e1veis aleat\u00f3rias cont\u00ednuas que se distribuem conjuntamente conforme a fun\u00e7\u00e3o de densidade&nbsp;<\/strong><strong>f(x,y)&nbsp;= x+y, na qual&nbsp;0 &lt; x &lt; 1&nbsp;e&nbsp;0 &lt; y &lt; 1.<\/strong><\/p>\n\n\n\n<p><strong>Com base nessas informa\u00e7\u00f5es, julgue os itens seguintes.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"347\" height=\"64\" src=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/05\/25210316\/image-692.png\" alt=\"\" class=\"wp-image-751239\" srcset=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/05\/25210316\/image-692.png 347w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/05\/25210316\/image-692-300x55.png 300w\" sizes=\"auto, (max-width: 347px) 100vw, 347px\" \/><\/figure>\n\n\n\n<p><strong>Coment\u00e1rios:<\/strong><\/p>\n\n\n\n<p>A esperan\u00e7a condicionada apresenta a propriedade aditiva:<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"532\" height=\"93\" src=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/05\/25210431\/image-693.png\" alt=\"\" class=\"wp-image-751240\" srcset=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/05\/25210431\/image-693.png 532w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/05\/25210431\/image-693-300x52.png 300w\" sizes=\"auto, (max-width: 532px) 100vw, 532px\" \/><\/figure>\n\n\n\n<p>Sabendo que X=1\/2, a esperan\u00e7a E(X|X=1\/2) corresponde \u00e0 esperan\u00e7a da constante X=1\/2:<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"233\" height=\"83\" src=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/05\/25210451\/image-694.png\" alt=\"\" class=\"wp-image-751241\" \/><\/figure>\n\n\n\n<p>Logo, a esperan\u00e7a desejada \u00e9:<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"413\" height=\"89\" src=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/05\/25210459\/image-695.png\" alt=\"\" class=\"wp-image-751242\" srcset=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/05\/25210459\/image-695.png 413w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/05\/25210459\/image-695-300x65.png 300w\" sizes=\"auto, (max-width: 413px) 100vw, 413px\" \/><\/figure>\n\n\n\n<p>A esperan\u00e7a de Y condicionada a X = 1\/2 \u00e9 definida como:<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"427\" height=\"92\" src=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/05\/25210547\/image-696.png\" alt=\"\" class=\"wp-image-751243\" srcset=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/05\/25210547\/image-696.png 427w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/05\/25210547\/image-696-300x65.png 300w\" sizes=\"auto, (max-width: 427px) 100vw, 427px\" \/><\/figure>\n\n\n\n<p>Em que&nbsp;f(y|X=1\/2)&nbsp;\u00e9 a raz\u00e3o entre a fun\u00e7\u00e3o densidade de probabilidade conjunta e a fun\u00e7\u00e3o densidade de probabilidade marginal de&nbsp;X=1\/2:<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"332\" height=\"104\" src=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/05\/25210558\/image-697.png\" alt=\"\" class=\"wp-image-751244\" srcset=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/05\/25210558\/image-697.png 332w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/05\/25210558\/image-697-300x94.png 300w\" sizes=\"auto, (max-width: 332px) 100vw, 332px\" \/><\/figure>\n\n\n\n<p>A fun\u00e7\u00e3o marginal de&nbsp;x \u00e9 calculada por:<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"261\" height=\"105\" src=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/05\/25210644\/image-698.png\" alt=\"\" class=\"wp-image-751245\" \/><\/figure>\n\n\n\n<p>Sabendo que&nbsp;0&lt;y&lt;1, temos:<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"764\" height=\"197\" src=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/05\/25210730\/image-699.png\" alt=\"\" class=\"wp-image-751246\" srcset=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/05\/25210730\/image-699.png 764w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/05\/25210730\/image-699-300x77.png 300w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/05\/25210730\/image-699-610x157.png 610w\" sizes=\"auto, (max-width: 764px) 100vw, 764px\" \/><\/figure>\n\n\n\n<p>Ent\u00e3o, o valor de&nbsp;f(X=1\/2)&nbsp;\u00e9:<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"284\" height=\"101\" src=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/05\/25210748\/image-700.png\" alt=\"\" class=\"wp-image-751247\" \/><\/figure>\n\n\n\n<p>Portanto, a fun\u00e7\u00e3o de Y condicionada a&nbsp;X=1\/2 \u00e9:<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"358\" height=\"87\" src=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/05\/25210837\/image-701.png\" alt=\"\" class=\"wp-image-751248\" srcset=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/05\/25210837\/image-701.png 358w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/05\/25210837\/image-701-300x73.png 300w\" sizes=\"auto, (max-width: 358px) 100vw, 358px\" \/><\/figure>\n\n\n\n<p>Agora, podemos calcular a esperan\u00e7a de Y condicionada a&nbsp;X=1\/2:<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"727\" height=\"289\" src=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/05\/25210855\/image-702.png\" alt=\"\" class=\"wp-image-751249\" srcset=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/05\/25210855\/image-702.png 727w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/05\/25210855\/image-702-300x119.png 300w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/05\/25210855\/image-702-610x242.png 610w\" sizes=\"auto, (max-width: 727px) 100vw, 727px\" \/><\/figure>\n\n\n\n<p>Por fim, somamos a esperan\u00e7a de X condicionada a X = 1\/2:<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"570\" height=\"86\" src=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/05\/25210927\/image-703.png\" alt=\"\" class=\"wp-image-751250\" srcset=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/05\/25210927\/image-703.png 570w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/05\/25210927\/image-703-300x45.png 300w\" sizes=\"auto, (max-width: 570px) 100vw, 570px\" \/><\/figure>\n\n\n\n<p>O resultado \u00e9 <strong>diferente<\/strong> de&nbsp;14\/12.<\/p>\n\n\n\n<p><strong>Observa\u00e7\u00e3o<\/strong>: em vez de utilizar a propriedade da esperan\u00e7a para separar a soma da esperan\u00e7a condicionada solicitada na quest\u00e3o, \u00e9 poss\u00edvel calcul\u00e1-la utilizando a pr\u00f3pria integral da esperan\u00e7a condicionada:&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"487\" height=\"80\" src=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/05\/25211137\/image-705.png\" alt=\"\" class=\"wp-image-751252\" srcset=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/05\/25211137\/image-705.png 487w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/05\/25211137\/image-705-300x49.png 300w\" sizes=\"auto, (max-width: 487px) 100vw, 487px\" \/><\/figure>\n\n\n\n<p>Sabendo que&nbsp;X=1\/2, temos:<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"783\" height=\"185\" src=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/05\/25211146\/image-706.png\" alt=\"\" class=\"wp-image-751253\" srcset=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/05\/25211146\/image-706.png 783w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/05\/25211146\/image-706-300x71.png 300w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/05\/25211146\/image-706-768x181.png 768w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/05\/25211146\/image-706-610x144.png 610w\" sizes=\"auto, (max-width: 783px) 100vw, 783px\" \/><\/figure>\n\n\n\n<p>Com isso, obtemos o mesmo resultado encontrado anteriormente.<\/p>\n\n\n\n<p>Assim, entendemos ser cab\u00edvel <strong>recurso<\/strong> pleiteando a <strong>altera\u00e7\u00e3o de gabarito <\/strong>de &#8220;certo&#8221; para &#8220;<strong>ERRADO<\/strong>&#8220;. <\/p>\n","protected":false},"excerpt":{"rendered":"<p>Oi pessoal! Tudo bem? O gabarito preliminar da PF saiu h\u00e1 pouco e acreditamos que existe possibilidade de recurso para uma quest\u00e3o. \u00c9 a quest\u00e3o do bloco 40 &#8211; 42 que trata da esperan\u00e7a condicionada. Aqui, vou resolver a quest\u00e3o de forma mais t\u00e9cnica e direta, utilizando 2 formas de resolu\u00e7\u00e3o diferentes, no intuito de [&hellip;]<\/p>\n","protected":false},"author":2036,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"post_tipo":"article","footnotes":""},"categories":[1],"tags":[],"tax_estado":[],"class_list":["post-751231","post","type-post","status-publish","format-standard","hentry","category-cursos-e-concursos"],"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>Recurso de Estat\u00edstica para Prova PF<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.estrategiaconcursos.com.br\/blog\/recurso-de-estatistica-para-prova-pf\/\" \/>\n<meta property=\"og:locale\" content=\"pt_BR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Recurso de Estat\u00edstica para Prova PF\" \/>\n<meta property=\"og:description\" content=\"Oi pessoal! Tudo bem? O gabarito preliminar da PF saiu h\u00e1 pouco e acreditamos que existe possibilidade de recurso para uma quest\u00e3o. \u00c9 a quest\u00e3o do bloco 40 &#8211; 42 que trata da esperan\u00e7a condicionada. Aqui, vou resolver a quest\u00e3o de forma mais t\u00e9cnica e direta, utilizando 2 formas de resolu\u00e7\u00e3o diferentes, no intuito de [&hellip;]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.estrategiaconcursos.com.br\/blog\/recurso-de-estatistica-para-prova-pf\/\" \/>\n<meta property=\"og:site_name\" content=\"Estrat\u00e9gia Concursos\" \/>\n<meta property=\"article:published_time\" content=\"2021-05-26T00:19:13+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2021-05-26T00:30:41+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/www.estrategiaconcursos.com.br\/blog\/wp-content\/uploads\/2021\/05\/image-692.png\" \/>\n<meta name=\"author\" content=\"Luana Brand\u00e3o\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@EstratConcursos\" \/>\n<meta name=\"twitter:site\" content=\"@EstratConcursos\" \/>\n<meta name=\"twitter:label1\" content=\"Escrito por\" \/>\n\t<meta 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Tudo bem? O gabarito preliminar da PF saiu h\u00e1 pouco e acreditamos que existe possibilidade de recurso para uma quest\u00e3o. \u00c9 a quest\u00e3o do bloco 40 &#8211; 42 que trata da esperan\u00e7a condicionada. 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