(a) Let [N(t), 1 0] be a nonhomogeneous Poisson process with mean value function m(r). Given N(t) =n, show that the unordered set of arrival times has the same distribution as n independent and identically distributed random variables having distribution function m(x) F(x)=m(t) x>1

(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(r) be the number of workers who are out of work at time t. By using part (a), find E[X(r)].