1. (30 points) Let N = {N(t), t 0} be a Poisson process on R+ with rate A>0. Let 0 < T T2 ... be the occurrence times and Tn = In-In-1 be the inter-occurrence times for n N where To = 0. Let J J2 = (2,7]. Compute the following. (a) P{N(J) = k}. (b) E[N(J2) | N(J) = 0]. (c) P{T >rs, T2 > t | T1 > r}. = (0,3] and