Let {Xn, n = 0, 1, 2, . . .} be a three-state Markov chain with S = {0, 1, 2} and the transition probability matrix Г0.1 0.3 0.67 P = 0.7 0.3 0 0.5 0 0.5 State 0 represents an operating state of some system, while states 1 and 2 represent repair states (corresponding to two types of failures). We assume that the process begins in state ✗0 = 0, and then the successive returns to state 0 from the repair state form a renewal process. Determine the mean duration of one of these renewal intervals. E[renewal interval]: =

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A: Given,

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Q: Please do question 1b, 1c and 1d with full working out. I'm struggling to understand what to write

A: The solution of the question is given below:

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A: Given that,to find  we will use matrix multiplication method.

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A: From the given information, Consider, the probability vector at stage 1 is,