Atotal of m white and m black balls are distributed among two urns, with each urn containing m balls. at each stage, a ball is randomly selected from each urn and the two selected balls are interchanged. let xn denote the number of black balls in urn 1 after the nth interchange.

(a) give the transition probabilities of the markov chain xn, n 0.
(b) without any computations, what do you think are the limiting probabilities of this chain?
(c) find the limiting probabilities and show that the stationary chain is time reversible.