6. Suppose that a customer of the system spends the amount of timeI mage waiting in queue before entering service.

(a) Show that, conditional on the preceding, the number of other customers that were in the system when the customer arrived is distributed as Image, where P is a Poisson random variable with mean λ.

(b) Let denote the amount of time that an customer spends in queue. As a by-product of your analysis in part (a), show that Image