Assume that a computer system is in one of three states: busy, idle, or

Chapter 7, Problem 2

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Assume that a computer system is in one of three states: busy, idle, or undergoingrepair, respectively denoted by states 0, 1, and 2. Observing its state at 2 P.M.each day, we believe that the system approximately behaves like a homogeneousMarkov chain with the transition probability matrix:P =0.6 0.2 0.20.1 0.8 0.10.6 0.0 0.4.Prove that the chain is irreducible, and determine the steady-state probabilities.

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