81.

(a) Let Image be a nonhomogeneous Poisson process with mean value function Image. Given Image, show that the unordered set of arrival times has the same distribution as n 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 Image. Suppose further that each injured man is out of work for a random amount of time having distribution F. Let Image be the number of workers who are out of work at time t. By using part (a), find .