7.4.5 A Markov chain X0;X1;X2; : : : has the transition probability matrix

A sojourn in a state is an uninterrupted sequence of consecutive visits to that state.

(a) Determine the mean duration of a typical sojourn in state 0.

(b) Using renewal theory, determine the long run fraction of time that the process is in state 1.

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012 0 0.3 0.7 0 P = 1 0.6 0 0.4 2 0 0.5 0.5