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The lifetime in months of a certain part has a gamma

Probability and Statistical Inference | 9th Edition | ISBN: 9780321923271 | Authors: Robert V. Hogg, Elliot Tanis, Dale Zimmerman ISBN: 9780321923271 41

Solution for problem 18E Chapter 5.3

Probability and Statistical Inference | 9th Edition

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Probability and Statistical Inference | 9th Edition | ISBN: 9780321923271 | Authors: Robert V. Hogg, Elliot Tanis, Dale Zimmerman

Probability and Statistical Inference | 9th Edition

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Problem 18E

Problem 18E

The lifetime in months of a certain part has a gamma distribution with α = θ = 2. A company buys three such parts and uses one until it fails, replacing it with a second part. When the latter fails, it is replaced by the third part.What are the mean and the variance of the total lifetime (the sum of the lifetimes of the three parts) associated with this situation?

Step-by-Step Solution:

Step 1 of 4

Given

Gamma distribution of

Let us assume that the three bought parts  are independent Each of these parts has the distribution of

Step 2 of 4

Chapter 5.3, Problem 18E is Solved
Step 3 of 4

Textbook: Probability and Statistical Inference
Edition: 9
Author: Robert V. Hogg, Elliot Tanis, Dale Zimmerman
ISBN: 9780321923271

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The lifetime in months of a certain part has a gamma