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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?

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...
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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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