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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 1minute period. Soln : Let Y be the number of students arrive at the centre in a 1minute 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 1minute 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 onehour 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.
 Fall '06
 various
 Probability

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