fall 2005 STAT 230 test3soln

# fall 2005 STAT 230 test3soln - STAT 230 Test #3 October 25,...

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Unformatted text preview: STAT 230 Test #3 October 25, 2005 4:30 – 5:15 pm 1. During scheduled office hours students come to the Tutorial Centre according to a Poisson process, with an average of one student every three minutes. [4] (a) Find the probability that two or more students visit in a particular 1-minute period. Soln : Let Y be the number of students arrive at the centre in a 1-minute period, then Y ∼ Poisson (1 / 3). P ( Y ≥ 2) = 1- P ( Y = 0)- P ( Y = 1) = 1- exp(- 1 / 3)- (1 / 3)exp(- 1 / 3) = . 045. [4] (b) Suppose we partition an hour into 60 consecutive 1-minute intervals. We call an interval ”Busy” if two or more students arrive at the centre during it. Give an expression for the probability that exactly 3 intervals are Busy in a one-hour period. Soln : This is a Binomial probability with x = 3, n = 60 and p = 0 . 045, i.e., ( 60 3 ) p 3 (1- p ) 57 . [4] (c) Use a suitable approximation to compute the probability in (b). Soln : Since n is big and p is small, the probability in (b) can be approximated by a Poisson probability with μ = np = 2 . 7, i.e., (2 . 7 3 / 3!)exp(- 2 . 7) = 0 . 22....
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## This note was uploaded on 03/03/2010 for the course STAT 230 taught by Professor Various during the Fall '06 term at Waterloo.

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fall 2005 STAT 230 test3soln - STAT 230 Test #3 October 25,...

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