4 9 Let fXng be a Markov chain with the state space f1 2 3g and transition probability matrix P 5 0 0 4 0 6 0 25 0 75 0 0 4 00 6 2 4 3 5 Let the initial distribution be p0 5 p10 p20 p30 5 0 4 0 2 0 4 Calculate the following probabilities a PX1 5 2 X3 5 2 X3 5 1jX0 5 1 b PX1 5 2 X3 5 2 X3 5 1 c PX1 ...

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4.9 Let fXng be a Markov chain with the state space f1; 2; 3g and transition probability...

Question:

4.9 Let fXng be a Markov chain with the state space f1; 2; 3g and transition probability matrix P 5 0 0:4 0:6 0:25 0:75 0 0:4 00:6 2 4 3 5 Let the initial distribution be pð0Þ 5 ½p1ð0Þ; p2ð0Þ; p3ð0Þ 5 ½0:4; 0:2; 0:4. Calculate the following probabilities:

a. P½X1 5 2; X3 5 2; X3 5 1jX0 5 1

b. P½X1 5 2; X3 5 2; X3 5 1

c. P½X1 5 2; X4 5 2; X6 5 2

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