The average number of customers arriving at a bank branch is eight per hour. Assume that customer arrivals follow a Poisson process. The bank opens at 9:00 am in the morning. Answer the following questions accordingly.
a) What is the probability that the first customer will arrive after 9:10 am?
b) Suppose that it is now 9:15 and the first customer has arrived at 9:12 am. What is the probability that the second customer will arrive after 9:25 am?
c) What is the probability that the third customer arrives exactly at 9:45 am?
d) What is the probability that exactly three customers arrive by 9:45 am?
Note in each case, we computed rate parameter of Poisson RV by considering the appropriate time intervals in minutes unit and given rate of 8 per hr as 8 per 60 mins.
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