Lista 2 (Probabilidade e Estatística).pdf

Lista 2 (Probabilidade e Estatística).pdf - Probabilidade...

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Probabilidade e Estat´ ıstica - Lista 2 Giannini Italino August 28, 2018 [1] Suponha que uma moeda honesta ´ e lan¸cada at´ e que um cara apare¸ ca pela primeira vez. Seja X o n´umero de lan¸ camentos at´ e que isso aconte¸ca. Obtenha a fun¸ ao de probabilidade de X . (Observe que, pelo menos teoricamente, X pode assumir um n´umero infinito de valores.) [2] Um sistema de inspe¸ ao ´ optica deve distinguir diferentes tipos de pe¸ cas. A probabilidade de uma classifica¸c˜ ao correta de qualquer pe¸ca ´ e 0 . 98. Suponha que trˆ es pe¸cas sejam inspecionadas e que as classifica¸c˜ oes sejam independentes. Seja a vari´ avel aleat´ oria X o n´umero de pe¸ cas classificadas corretamente. De- termine a fun¸ ao de probabilidade de X . [3] Seja X uma vari´ avel aleat´ oria discreta e seja f uma fun¸c˜ ao tal que x 1 2 3 4 5 f ( x ) p 2 p 2 p p p 2 (a) Encontre o valor de p de modo que f seja uma fun¸ ao de probabilidade. (b) Calcule P ( X 4) e P ( X < 3). (c) Calcule P ( | X - 3 | ≥ 2). (d) Obtenha E ( X ) e V ar ( X ). [4] Suponha que falhas em determinada m´ aquina ocorram com mesma frequˆ encia. Dependendo do tipo de falha, o t´ ecnico pode levar 1, 2, 3, 4 ou 5 horas para concertar a m´ aquina. (a) Descreva o modelo probabil´ ıstico apropriado para representar a dura¸c˜ ao do tempo de concerto da m´ aquina?
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  • Spring '14
  • Byte, ppm, C˜, Suponha, Número CAS

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