4. Consider a process {Xn, n = 0, 1, . . .}, which takes on the values 0, 1, or 2. Suppose

where 2j =0 PI ij = 2j =0PII ij = 1, i = 0, 1, 2. Is {Xn, n 0} a Markov chain? If not, then show how, by enlarging the state space, we may transform it into a Markov chain.

P(X+1= |X=1, Xn-1=in-1,..., X0=10} P! ij when n is even pll ij, when " is odd