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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.

Algebra: Structure And Method, Book 1
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter7: Applying Fractions
Section7.5: Percents
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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.

파 2 3
Transcribed Image Text:파 2 3
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