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

Suppose P{Xn+1 = j |Xn = i,Xn−1 = in−1,...,X0 = i0}

=

PI ij , when n is even PII ij , when n is odd where 2 j=0 PI ij = 2 j=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.