Consider a process (X,, n = 0, 1,...] which takes on the values 0, 1, or 2.

Suppose P{X+1=j|X, i, X-in-1 X = i0] = where PoP 1, PH, when n is even when n is odd 0, 1, 2.

Is (X, n 0) a Markov chain? If not, then show how, by enlarging the state space, we may transform it into a Markov chain.