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

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
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) =
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

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.

Page1 / 2

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online