A system consists of five components is connected in series as shown below.345As soon as one component fails, the entire system will fail. Assume that the components fail independently ofone another.(a) Suppose that each of the first two components have lifetimes that are exponentially distributed with mean 103weeks, and that each of the last three components have lifetimes that are exponentially distributed with mean130 weeks. Find the probability that the system lasts at least 55 weeks.(b) Now suppose that each component has a lifetime that is exponentially distributed with the same mean. Whatmust that mean be (in years) so that 92% of all such systems lasts at least one year?

Part (a)Let's denote the lifetime of the components as follows:- X1 and X2 are the lifetimes of…

Answered: A system consists of five components is…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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