(a) Let {N(t), 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 n independent and identically distributed random variables having distribution function F(x)= m(x) m(t) x t x>1

(b) Suppose that workers incur accidents in accordance with a nonho- mogeneous Poisson process with mean value function m(t). Suppose further that each injured person 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 Compute E[X(t)] and Var(x(t)).