# Suppose that in Problem 17, the components are in parallel, so that the system will fail only…

Suppose that in Problem 17, the components are in parallel, so that the system will fail only when all the components fail. Find the p.d.f. of T, and then find the probability P(T > 15).

Problem 17

A mechanical system has three components in series, so the system will fail when at least one of the components fails. The random variables X1,X2, and X3 represent the lifetime of these components. Suppose that the Xi(i = 1, 2, 3) are independently and identically distributed as exponential with parameter λ = 0.1. Let the random variable T denote the lifetime of the system. Find the p.d.f. of T, and then find the probability P(T > 10).

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