Customers arrive at a bank at a Poisson rate of λ. Let M(t) be the number of customers who enter the bank by time t only to make deposits to their accounts. Suppose that, independent of other...

Customers arrive at a bank at a Poisson rate of λ. Let M(t) be the number of customers who enter the bank by time t only to make deposits to their accounts. Suppose that, independent of other customers, the probability is p that a customer enters the bank only to make a deposit. Show that $ M(t): t ≥ 0 % is a Poisson process with parameter λp.