4.2. Let {N(t); t ? 0} be a Poisson process of rate A, representing the arrival process of customers entering a store. Each customer spends a duration in the store that is a random variable with cumulative distribution function G. The customer durations are independent of each other and of the arrival process. Let X(t) denote the number of customers remaining in the store at time t, and let Y(t) be the number of customers who have arrived and departed by time t. Determine the joint distribution of X(t) and Y(t).