Let {X, n 0} be a Markov chain with stationary probabilities #,, j 0. Suppose that X = i and define T = Min{n: n > 0 and X = i}. Let YX, 0, 1, ., T. Argue that {Y,,j = 0, ., T} is distributed as the states of the reverse Markov chain (with transition probabilities PP/) starting in state 0 until it returns to 0