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Statistics / Probability and Statistical Inference 9 / Chapter 5.3 / Problem 5.3-18

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

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The lifetime in months of a certain part has a gamma distribution with = = 2. A company

Chapter 5, Problem 5.3-18

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QUESTION:

The lifetime in months of a certain part has a gamma distribution with = = 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?

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QUESTION:

The lifetime in months of a certain part has a gamma distribution with = = 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?

ANSWER:

Step 1 of 2

Given: Gamma distribution of

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

The mean of a gamma distribution is the product of its parameters:

The variance of a gamma distribution is the product of and the square of :

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