Question: A three- state Markov chain has the following transition matrix: (a) Does this Markov chain have a unique steady- state probability vector? If so, find

A three- state Markov chain has the following transition matrix:

(a) Does this Markov chain have a unique steady- state probability vector? If so, find it.
(b) What is the approximate value of p1 3 ,(100)? What interpretation do you give to this result?
(c) What is the probability that after the third step you are in state 3 if the initial state probability vector is (1/ 3 1/ 3 1/ 3)?

0.25 0.5 0.25 P = | 0.4 0.6 0

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