Question: Let X1, X2, X3 be independent random variables that represent lifetimes (in hours) of three key components of a device. Say their respective distributions are

Let X1, X2, X3 be independent random variables that represent lifetimes (in hours) of three key components of a device. Say their respective distributions are exponential with means 1000, 1500, and 2000. Let Y be the minimum of X1, X2, X3 and compute P(Y > 1000).

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