Question: 4.4.2 Consider the Markov chain whose transition probability matrix is given by (a) Determine the limiting probability 0 that the process is in state 0.

4.4.2 Consider the Markov chain whose transition probability matrix is given by

012 00 010 3 1 0.1 0.4 0.2 0.3 P = 2

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

(b) By pretending that state 0 is absorbing, use a first step analysis (Chapter 3, Section 3.4) and calculate the mean time m10 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 m0 D 1Cm10. Verify equation (4.26), 0 D 1=m0.

012 00 010 3 1 0.1 0.4 0.2 0.3 P = 2 0.2 0.2 0.5 0.1 3 0.3 0.3 0.4 0

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