Suppose you are a store owner and guess that, once you open the store, the time T in hours until your first customer of the day arrives is exponentially distributed with parameter = 4. With this same parameter, you also guess that the number of customers you will see in this hour is Poisson distributed.

(a) What is the expected rate of customers per hour?

(b) What is the expected number of minutes until the first customer arrives?

(c) Compute the probability that the first customer arrives later than 15 minutes but before 45minutes. Supply an exact answer.

(d) What is the probability that you see exactly 3 customers in the first hour? Supply an exact answer.