1. [Poisson Process] Let N = (Me; t > 0) be a Poisson process with rate A = 1. Find: (a) P(M1 2 1/N2 = 2). (b) P(N2 = 2|N1 2 1). 2. Poisson Process, cont.] For the Poisson Process in the previous problem, find: (a) The probability of 1 arrival in [0, 1] , 1 arrival in [1, 2] and 1 arrival in [2, 3]. (b) The probability of 2 arrivals in [0, 2] and 2 arrivals in [1, 3]. (c) The probability of 2 arrivals in [1, 2] given that there are 2 arrivals in [0, 2] and 2 arrivals in [1, 3]