Exercise 3.2. Let (Xn; n > 0) be a discrete-time Markov chain with a stationary distribution 7. Suppose that (Xn) is reversible with respect to . Show that for all integers n > 1 and states 10, 11, ... , in, it holds that P.(X, = 10, X1 = 11, . , X = in) =P (X, = in, X = in-1,.. , Xn = 10). Here under P, the PMF of X, is given by 7. Exercise 3.2. Let (Xn; n > 0) be a discrete-time Markov chain with a stationary distribution 7. Suppose that (Xn) is reversible with respect to . Show that for all integers n > 1 and states 10, 11, ... , in, it holds that P.(X, = 10, X1 = 11, . , X = in) =P (X, = in, X = in-1,.. , Xn = 10). Here under P, the PMF of X, is given by 7