Processes Stochastic and Probability Theory III Assignment #5. Due Wednesday, June 3 1. Let Pij = e-i ij , i, j = 0, 1, . . . be the transition probabilities for a Markov chain Xn . j! We consider P00 = 1. Verify that Xn is a martingale. 1 e(j-i)! 2. Let Xn be a Markov chain transition whose probabilities are Pij = 0, 1, . . . and j = i, i + 1, . . .. Verify the martingale property for (a) Yn = Xn - n 2 (b) Un = Yn - n for i = (c) Vn ...