4. (20%) Customers arrive at a service facility according to a Poisson process of rate A=2 customers/hour. Let X (t) be the number of customers that have arrived up to time t. Let W be the waiting time for the n-th customer, n = 1, 2, … … …. (a) Find E(X(4)X(5)|X(1) = 3). (b) Calculate E(X(1) + X(3)|X(2) = 3). (c) Find P(W+1 ≤ s|x(t) = k) for s > 0 and k > 0.

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