Let P^(1) and P^(2) denote transition probability matrices for ergodic Markov chains having the same state space. Let π^1 and π^2 denote the stationary (limiting) probability vectors for the two chains. Consider a proeess defined as follows: (i) X0=1 . A coin is then flipped and if it comes up heads, then the remaining states X1, …are obtained from the transition probability matrix P^(1) and if tails from the matrix P^(2) . Is {Xn, n ≥0} a Markov chain? If p=P coin comes up heads], what is limn

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