Customers arrive at a service facility according to a Poisson process of rate λ customers/hour. Let X(t) be the number of custom
ers that have arrived up to time t. Let W1,W2,... be the successive arrival times of the customers. (a) Determine the conditional mean E[W1|X(t)=2].
(b) Determine the conditional mean E[W3|X(t)=5].
(c) Determine the conditional probability density function for W2, given that X(t)=5.