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Let Xn be the Markov chain with states S = {1, 2, 3, 4} and transition...

Let Xn be the Markov chain with states S = {1, 2, 3, 4} and transition matrix.

1/3 2/3 0 0
2/3 0 1/3 0
1/3 1/3 0 1/3
0 1/3 2/3 0

a.) Let X0 = 3 and let T3 be the first time that the Markov chain returns 3, compute P(T3 = 2 given X0=3). Please show all work and all steps.

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