Two urns contain k balls each. Initially, the balls in the left urn are all red and the balls in the right urn are all blue. At each step, pick a ball at random from each urn and exchange them. Let X be the number of blue balls in the left turn. (Note that necessarily Xo 0 and X = 1.) (9) a) Argue that X b) Let k = = = (Xn, n0) is a Markov chain. (2) 4. Find the transition matrix of X. (4) Now find the transition matrix of X for an arbitrary k.(3)