Question: A Markov chain {X n : n = 0, 1, 2, . . .} has the transition probability matrix P = ( 0.5 0.4 0.1

A Markov chain {Xn : n = 0, 1, 2, . . .} has the transition probability matrix

P = ( 0.5 0.4 0.1

0.2 0.4 0.4

0.4 0.1 0.5 )

If it is known that the process starts in state 0, determine the probability P(X3 = 2).

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