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Consider the following finite-state Markov chain: 1. Let rij (n) denote the probability of the process ending up in state j in n transitions, conditioned

Consider the following finite-state Markov chain:

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1. Let rij (n) denote the probability of the process ending up in state j in n transitions, conditioned that the process started in state i. Find: (i)limn r1,2(n). (ii)limn r1,5(n). (iii)limn r1,7(n). (iv)limn r4,5(n).

2. Find all the steady state probabilities.

2/3 2 2 2/3 1/3 1/3 1/2 3 1/3 2/3 1 1/2 2/3 1/3 1/3 4 5 7 2/3 2/3 2 2 2/3 1/3 1/3 1/2 3 1/3 2/3 1 1/2 2/3 1/3 1/3 4 5 7 2/3

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