Let {N(t), t 0} be a renewal process and suppose that for all n and t conditional on the event that N(t) = n, the event times S,., S, are distributed as the order statistics of a set of independent uniform (0, t) random variables Show that {N(t), t 0} is a Poisson process (Hint Consider E[N(s) | N(t)] and then use the result of Problem 3.5.)