# Question

Reconsider Prob. 29.6-2. Now suppose that the manufacturer keeps a spare machine that only is used when the primary machine is being repaired. During a repair day, the spare machine has a probability of 0.1 of breaking down, in which case it is repaired the next day. Denote the state of the system by (x, y), where x and y, respectively, take on the values 1 or 0 depending upon whether the primary machine (x) and the spare machine (y) are operational (value of 1) or not operational (value of 0) at the end of the day.

(a) Construct the (one-step) transition matrix for this Markov chain.

(b) Find the expected recurrence time for the state (1, 0).

(a) Construct the (one-step) transition matrix for this Markov chain.

(b) Find the expected recurrence time for the state (1, 0).

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