A system consisting of five components will not function as long as one of the five components fails. Suppose that all components function independently and the time to failure of each component follows an exponential distribution with parameter 1. Let T denote the first time the system fails. (a) Find the probability density function of T. (b) If the five components are labelled as A,B,C,D, and E, what is the probability that the first failed component is not A?
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