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  3. 2 a continuous time markov chain consisting of two states...

Question: 2 a continuous time markov chain consisting of two states...

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2. (A continuous time Markov chain consisting of two states) Consider a machine that works for an exponential amount of time having mean 1/2 before breaking down, and suppose that it takes an exponential amount of time having mean 1/μ to repair the machine. If the machine is in working condition at time 0, then what is the probability that it will be working at time t 10? Hint: Consider that this case is a birth and death process, with state 0 meaning that the machine is working and state 1 that it is being repaired, having parameters

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