Question: 1.5. A Markov chain Xo, X,, X2, . . . has the transition probability matrix and initial distribution po = 0.5 and p, = 0.5.

1.5. A Markov chain Xo, X,, X2, . . . has the transition probability matrix

0 1 2 0 || 0.3 0.2 0.5 P 1 0.5 0.1

and initial distribution po = 0.5 and p, = 0.5. Determine the probabilities Pr(X0 = 1, X, = 1, X2 = 0} and Pr{X1 = 1, X2 = 1, X3 = 0}.

0 1 2 0 || 0.3 0.2 0.5 P 1 0.5 0.1 0.4 20.5 0.2 0.3

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