Question: A system has n components, whose lifetimes are exponential random variables with parameters 1, 2, . . . , n, respectively. Suppose that the lifetimes

A system has n components, whose lifetimes are exponential random variables with parameters λ1, λ2, . . . , λn, respectively. Suppose that the lifetimes of the components are independent random variables, and the system fails as soon as one of its components fails. Find the probability density function and the expected value of the time until the system fails.

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