Problem #8: A system consists of five components is connected in series as shown below. 3 5 As soon as one component fails, the entire system will fail. Assume that the components fail independently of one another. (a) Suppose that each of the first two components have lifetimes that are exponentially distributed with mean 90 weeks, and that each of the last three components have lifetimes that are exponentially distributed with mean 137 weeks. Find the probability that the system lasts at least 43 weeks. (b) Now suppose that each component has a lifetime that is exponentially distributed with the same mean. What must that mean be (in years) so that 94% of all such systems lasts at least one year?

Problem #8: A system consists of five components is connected in series as shown below. 3 5 As soon as one component fails, the entire system will fail. Assume that the components fail independently of one another. (a) Suppose that each of the first two components have lifetimes that are exponentially distributed with mean 90 weeks, and that each of the last three components have lifetimes that are exponentially distributed with mean 137 weeks. Find the probability that the system lasts at least 43 weeks. (b) Now suppose that each component has a lifetime that is exponentially distributed with the same mean. What must that mean be (in years) so that 94% of all such systems lasts at least one year?

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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