47.

(a) Let \N(i), t > 0} be a nonhomogeneous Poisson process with mean value function m(t). Given N(t) = n, show that the unordered set of arrival times has the same distribution as ç independent and identically distributed random variables having distribution function

(b) Suppose that workmen incur accidents in accordance with a nonhomogeneous Poisson process with mean value function m(t). Suppose further that each injured man is out of work for a random amount of time having distribution F. Let X(t) be the number of workers who are out of work at time t. By using part (i), find E[X(t)].