Devore [2010] Consider a system consisting of three components as pictured. The system will continue to function as long as the first component functions and either component 2 or component 3 functions. Let X1, X2, and X3 denote the lifetimes of components 1, 2, and 3, respectively. Suppose the Xi ’s are independent of one another and each Xi has an exponential distribution with parameter λ. (a) Let Y denote the system lifetime. Obtain the cumulative distribution function of Y and differentiate to obtain the pdf. [Hint: F(y) = P(Y ≤ y); express the event {Y ≤ y} in terms of unions and/or intersections of the three events {X1 ≤ y}, {X2 ≤ y}, and {X3 ≤ y}.] (b) Compute the expected system lifetime.

Devore [2010] Consider a system consisting of three components as pictured. The system will continue to function as long as the first component functions and either component 2 or component 3 functions. Let X1, X2, and X3 denote the lifetimes of components 1, 2, and 3, respectively. Suppose the Xi ’s are independent of one another and each Xi has an exponential distribution with parameter λ. (a) Let Y denote the system lifetime. Obtain the cumulative distribution function of Y and differentiate to obtain the pdf. [Hint: F(y) = P(Y ≤ y); express the event {Y ≤ y} in terms of unions and/or intersections of the three events {X1 ≤ y}, {X2 ≤ y}, and {X3 ≤ y}.] (b) Compute the expected system lifetime.

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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