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5.27 An unreliable electronic system has two components hooked up in parallel. The lifetimes X and Y of the two components have the joint density f(x, y) = e for 0 < x≤ y < oo. The system goes down when both components have failed. What is the joint density of X and Y - X? What are the marginal densities of X and Y - X? What is the density function of the time until the system goes down?

5.27 An unreliable electronic system has two components hooked up in parallel. The lifetimes X and Y of the two components have the joint density f(x, y) = e for 0 < x≤ y < oo. The system goes down when both components have failed. What is the joint density of X and Y - X? What are the marginal densities of X and Y - X? What is the density function of the time until the system goes down?

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.CR: Chapter 13 Review
Problem 29CR
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questions number 5.27

5.3 Marginal Probability Densities 221 5.27 An unreliable electronic system has two components hooked up in parallel. The lifetimes X and Y of the two components have the joint density f(x, y) = ey for 0 < x≤ y < oo. The system goes down when both components have failed. What is the joint density of X and Y-X? What are the marginal densities of X and Y - X? What is the density function of the time until the system goes down? 5.3.1 Independence of Jointly Distributed Random Variables A general condition for the independence of the jointly distributed random variables X and Y is stated in Definition 3.2. In terms of the marginal densities, the continuous analogue of Rule 3.7 for the discrete case is: Rule 5.2 The jointly distributed random variables X and Y are independent
Transcribed Image Text:5.3 Marginal Probability Densities 221 5.27 An unreliable electronic system has two components hooked up in parallel. The lifetimes X and Y of the two components have the joint density f(x, y) = ey for 0 < x≤ y < oo. The system goes down when both components have failed. What is the joint density of X and Y-X? What are the marginal densities of X and Y - X? What is the density function of the time until the system goes down? 5.3.1 Independence of Jointly Distributed Random Variables A general condition for the independence of the jointly distributed random variables X and Y is stated in Definition 3.2. In terms of the marginal densities, the continuous analogue of Rule 3.7 for the discrete case is: Rule 5.2 The jointly distributed random variables X and Y are independent
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