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A machine is subject to shocks arriving from two independent sources. The shocks from source 1...

A machine is subject to shocks arriving from two independent sources. The shocks from source 1 arrive according to a Poisson process with rate 6 per day and those from source 2 at a rate 4 per day. Suppose a shock from source 1 can cause the machine to fail with probability p1 = 0.1, and a shock from source 2 can cause the machine to fail with probability p2 = 0.5. A failed machine is replaced instantaneously. Let N(t) be the number of machine replacements over the interval (0, t]. Is {N(t), t ≥ 0} a Poisson process? If so, what is its parameter?

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