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 process 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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Let 𝐏 and 𝐐 be transition probability matrices on states 1, …, m, with respective transition probabilities Pi, j and Qi, j. Consider processes {Xn, n ≥0} and {Yn, n ≥0} defined as follows: (a) X0=1. A coin that comes up heads with probability p is then flipped. If the coin lands heads, the subsequent states X1, X2, …, are obtained by using the transition probability matrix 𝐏; if it lands tails, the subsequent states X1, X2, …, are obtained by using the transition probability matrix 𝐐. (In ot