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The following is the transition probability matrix of a Markov chain with states 1,2,3,4 𝐏=( .4 .3 .2 .1 .2 .2 .2 .4 .25 .25 .5 0 .2 .1 .4 .3) If X0=1 (a) find the probability that state 3 is entered before state 4 ; (b) find the mean number of transitions until either state 3 or state 4 is entered. | Numerade

Let P be the transition probability matrix of a Markov chain. A... | Filo

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