The Ehrenfest model for heat exchange can be described as follows: two urns, A and B, contain a total of 2N balls. At every step, each ball is equally likely to be drawn form among all the 2N balls. It is then put into the other urn. Let Xn be the number of balls in urn A immediately after the nth step. (a) Show that X0, X1, X2, . . . is a Markov Chain and nd the transition probability matrix. (b) Let [14,71 = E[Xn|X0 = 2], 2 = 0,. . . ,2N. ShOW that \"Jim 2 1 + (1 1/N)Hi,n11 for all n > 0. (c) Show that m = N + (2' N)