39. A system consists of two independent machines that each function for an exponential time with rate
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39. A system consists of two independent machines that each function for an exponential time with rate λ. There is a single repairperson.
If the repairperson is idle when a machine fails, then repair immediately begins on that machine; if the repairperson is busy when a machine fails, then that machine must wait until the other machine has been repaired. All repair times are independent with distribution function G and, once repaired, a machine is as good as new. What proportion of time is the repairperson idle?
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