# Tutorial_8 - STAT 333 Tutorial 8 Nov. 29, 2010 1. Customers...

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STAT 333 Tutorial 8 Nov. 29, 2010 1. Customers enter a department store according to a Poisson process { N ( t ) ,t 0 } at rate λ = 10 per hour. Of the entering customers, suppose that 70% of them are female and the remaining 30% are male. Assume that customers are independent of one another. (a) During the ﬁrst hour of the store’s operation, what is the probability that exactly 3 males and exactly 6 females enter the store? Let N 1 ( t ) represent the number of female customers entering the store by time t . Let N 2 ( t ) represent the number of male customers entering the store by time t . We know that N 1 ( t ) is Poisson distributed with mean 10 × 0 . 7 t = 7 t and N 2 ( t ) is Poisson distributed with mean 10 × 0 . 3 t = 3 t . Since N 1 ( t ) and N 2 ( t ) are independent, P ( N 1 (1) = 6 ,N 2 (1) = 3) = P ( N 1 (1) = 6) P ( N 2 (1) = 3) = e - 7 (7) 6 6! e - 3 (3) 3 3! = 0 . 0334 (b) If S n denotes the time that the n -th customer enters the store, calculate E [ S 9 | N (0 . 5) =

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## This note was uploaded on 01/19/2011 for the course STATISTICS STAT 333 taught by Professor Menzhongxian during the Fall '10 term at Waterloo.

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Tutorial_8 - STAT 333 Tutorial 8 Nov. 29, 2010 1. Customers...

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