1.Customers arrive in a certain shop according to an approximate Poisson process at a mean rate of 10 per hour. Let W denote the waiting time in minutes until the first two customers arrive.

(a) How is W distributed?

(b) What is the probability density function of W.

(c) What is the probability that the shopkeeper will have to wait less than 10 minutes for two customers to arrive.

2.Let Z Exp(mean ). Derive E(Z) and Var(Z) using the MGF.