2. Assume that the number of taxis that arrive at a busy intersection follows a

Question

2. Assume that the number of taxis that arrive at a busy intersection follows a Poisson distribution with a mean of 6 taxis per hour. Let X denote the time between arrivals of taxis at the intersection. (a) What is the mean of X? (b) What is the probability that you wait longer than one hour for a taxi? (c) Suppose that you have already been waiting for one hour for a taxi. What is the probability that one arrives within the next 10 minutes? (d) Determine x such that the probability that you wait more than x minutes is 0.10. (e) Determine x such that the probability that you wait less than x minutes is 0.90

Explanation / Answer

a) lambda = 6

Hence mean of X = 6 where X~P(6)

b) P(X>1) = 1- P(X<=1) = 1- P(X=0) - P(X=1) = 1- (e(-6)*6^0) - ( (e(-6)*6) = 0.982

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