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Suppose passengers arrive at a MARTA station between 10am-5pm following a Poisson process with rate λ=...

Suppose passengers arrive at a MARTA station between 10am-5pm following a Poisson process with rate λ= 60 per hour. For notation, let N(t) be the number of passengers arrived in the first t hours, S0= 0 , Sn be the arrival time of the nth passenger, Xn be the interrarrival time between the (n−1)st and nth passenger.

a. What is the probability that ten passengers arrive between 2pm and 4pm given that no customer

arrive in the first half hour?

b. What is the average time of the first arrival?

c. What is the expected time of the thirtieth arrival?

Math   Statistics-And-Probability   
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