4.2. Consider the Markov chain whose transition probability matrix is given by

(a) Determine the limiting probability .7ro that the process is in state 0.

(b) By pretending that state 0 is absorbing, use a first step analysis (III, Section 4) and calculate the mean time m,0 for the process to go from state 1 to state 0.

(c) Because the process always goes directly to state 1 from state 0, the mean return time to state 0 is m = 1 + m,,,. Verify equation (4.5), ir = 1/NO.

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P = 2 0 1 2 3 0 1 0 0 0.1 0.4 0.2 0.3 0.2 0.2 0.2 0.5 0.1 3 | 0.3 0.3 0.3 0.4 0