5.4.2 Let fN.t/I t  0g be a Poisson process of rate , 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/.