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28 A piece of equipment is subject to random failures. The time-to-failure ran- dom variable follows an exponential distribution with mean 1/2. When the equipment

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28 A piece of equipment is subject to random failures. The time-to-failure ran- dom variable follows an exponential distribution with mean 1/2. When the equipment fails, it will be repaired. The repair time follows an exponential distribution with mean 1/u. The times to failure and repair times are all mutually independent. Thus the state of the equipment alternates between working and being repaired. Assume that at time 0 the equipment is work- ing. Let M() denote the number of failures by time t. Find an approximation of E[M(1) ] for large t

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