(Answered) Question there are m machines in a factory operating

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Question: There are m machines in a factory operating independently. Each machine works for a time period that is exponentially distributed with mean 1/µ. Then it breaks down. The time that it takes to repair an out-of-order machine is exponential with mean 1/λ, independent of repair times for and operating times of other machines. For 0 ≤ i ≥ m, ?nd the long-run proportion of time that there are exactly I machines operating.

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