Question: 3.7.2 Consider the random walk Markov chain whose transition probability matrix is given by The transition probability matrix corresponding to the nonabsorbing states is Calculate

3.7.2 Consider the random walk Markov chain whose transition probability matrix is given by

0 1 2 3 1 0 0 0 1 0.3 0 0.7

The transition probability matrix corresponding to the nonabsorbing states is

0 P = 2 0 0.3 0 0.7 3 0 00 1

Calculate the matrix inverse to I????Q, and from this determine

(a) the probability of absorption into state 0 starting from state 1;

(b) the mean time spent in each of states 1 and 2 prior to absorption

0 1 2 3 1 0 0 0 1 0.3 0 0.7 0 P = 2 0 0.3 0 0.7 3 0 00 1

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