# 28. Consider n components with independent lifetimes, which are such that component i functions for an exponential

## Question:

28. Consider n components with independent lifetimes, which are such that component i functions for an exponential time with rate λi . Suppose that all components are initially in use and remain so until they fail.

**(a)** Find the probability that component 1 is the second component to fail.

**(b)** Find the expected time of the second failure.

Hint: Do not make use of part (a).

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