Question: 2.7. Consider a machine whose condition at any time can be observed and classified as being in one of the following three states: State 1:

2.7. Consider a machine whose condition at any time can be observed and classified as being in one of the following three states:

State 1: Good operating order State 2: Deteriorated operating order State 3: In repair We observe the condition of the machine at the end of each period in a sequence of periods. Let X denote the condition of the machine at the end of period n for n = 1, 2..... Let X0 be the condition of the machine at the start. We assume that the sequence of machine conditions is a Markov chain with transition probabilities

P = 0.9, P = 0.1, P3 = 0, P21 = 0,

and that the process starts in state Xo = 1.

(a) Find Pr(X4 = 1).

(b) Calculate the limiting distribution.

(c) What is the long run rate of repairs per unit time?

P = 0.9, P = 0.1, P3 = 0, P21 = 0, P22 = 0.9, P = 0.1, P = 1, P32 = 0, P = 0,

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