An exponential distribution with parameter

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A factory has m machines. Each machine fails at an exponential rate μ. When a machine fails, it remains down during a random time having an exponential distribution with parameter λ. Moreover, the machines are independent mfrom one another. Let X{t) be the number of machines that are in working order at time t > 0. It can be shown that the stochastic process {X{t),t ≥ 0} is a birth and death process.

(a) Find the birth and death rates of the process {X{t), t > 0}.

(b) Show that

Reference no: EM131131060

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