Question

Suppose that buses are coming into a station at an average rate 4 per hour according...

Suppose that buses are coming into a station at an average rate 4 per hour according to a Poisson process. We start to account the buses from 1:00 (pm).

(a) What is the probability that no buses arrive between 1:00pm-2:00pm?
(b) What is the probability that three buses arrive between 1:00pm-3:00pm?
(c) What is the probability that the third bus takes more that 3 hours to arrive?

(d) What is the expected time the third bus arrive to the station?

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