Question

2. A Markov chain Xo, Xi, X2,. has transition matrix (6363es) 0 0.3 0.2 0.5 20.3 0.30.4 (i) Determine the conditional probabilities P(X1 = 1,X2 = 01X0 = 0), ( P(Xo = 1) = P(Xo = 2) 1/2· P= 1 | 0.5 0.1 0.4 P(X,-2X, = 0). 11) Suppose the initial distribution is Determine the probabilities P(Xo-1, X1 1, X22) and P(X3 0).

A Markov chain X0, X1, X2,... has transition matrix

012
0 0.3 0.2 0.5

P = 1  0.5 0.1 0.4 .2 0.3 0.3 0.4

(i) Determine the conditional probabilities P(X1 = 1,X2 = 0|X0 = 0),P(X3 = 2|X1 = 0).

(ii) Suppose the initial distribution is P(X0 = 1) = P(X0 = 2) = 1/2. Determine the probabilities P(X0 = 1, X1 = 1, X2 = 2) and P(X3 = 0).

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