A certain system is based on two indeperndent modules, A and B. A failure of any one of these modules causes a failre of the whole system. The lifetime of cach module has Exponential distribution with the following parameters. Modules A's lifetime. A - 0.100 years Modules B's lifetime: A = 0.250 years a. What is the probability that the system works at least 12 years without a failure? b. Given that the system failed during the first 12 years, what is the probability that it failed due to the failure of component 8 (but not component A)? Write your answers by providing 3 digits after the decimal point.

A certain system is based on two indeperndent modules, A and B. A failure of any one of these modules causes a failre of the whole system. The lifetime of cach module has Exponential distribution with the following parameters. Modules A's lifetime. A - 0.100 years Modules B's lifetime: A = 0.250 years a. What is the probability that the system works at least 12 years without a failure? b. Given that the system failed during the first 12 years, what is the probability that it failed due to the failure of component 8 (but not component A)? Write your answers by providing 3 digits after the decimal point.

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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Estimation

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Question

A certain systerm is based on two independent modules, A and B. A failure of any one of these modules causes a failure of the whcle system.
The lifetime of cach module has Exponential distribution with the folloing parameters.
Modules A's lifetime A = 0.100 years
Modules B's lifetime: A = 0.250 years
a. What is the probability that the system works at least 12 years without a failure?
b. Given that the system failed during the first 12 years, what is the probability that it failed due to the failure of component 8 (but not
component A)?
Write your answers by providing 3 digits after the decimal point.

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