Markov Chain: Understanding Higher-order Transition Matrix

Answered: 13. Which of the following is the transition matrix of an absorbing Markov chain? a [] » [1] • [4] 1/32/3 d) 23 1/31 13 23 1/2 1/2 e) none of the others | bartleby

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