# Repeat Problems 17 and 18, by supposing that the lifetimes of the three components are…

Repeat Problems 17 and 18, by supposing that the lifetimes of the three components are independently and identically distributed as Weibull with α = 2,β = 0.5.

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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