Exercise 2. Consider a sequence of random variables { X, : n 2 0}, which takes on the values 0, 1, or 2. Suppose when n is even, P(Xn+1 = ] | Xn = i, Xn-1 = in-1, ..., Xo = 10) = plI i, j : when n is odd, where 2 PH = pll ij =1, j=0 j=0 for i = 0, 1, 2. Is {Xn : n 2 0} a Markov chain? If not, then show how, by enlarging the state space, we may transform it into one