Homework Help is Here – Start Your Trial Now!
Math
Probability
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)
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...
See similar textbooks
icon
Related questions
Question

Please show a step-by-step solution. Do not skip steps, and explain your steps. Write it on paper, preferably. Make sure the work is clear.

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. Problem #8(a): Problem #8(b): 2 (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? Round your answer to 4 decimals. Answer in years, correct to 2 decimals
Transcribed Image Text: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. Problem #8(a): Problem #8(b): 2 (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? Round your answer to 4 decimals. Answer in years, correct to 2 decimals
Expert Solution
steps

Step by step

Solved in 4 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer