Question: A Markov chain {Xn, n 0} with states 0, 1, 2, has the transition probability matrix 1 2 1 3 1

A Markov chain {Xn, n 0} with states 0, 1, 2, has the transition probability matrix

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⎢

⎢

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1 2

1 3

1 6

0 1 3

2 3

1 2 0 1 2

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⎥

⎥

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If P{X0 = 0} = P{X0 = 1} = 1 4 , find E[X3].

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