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Probability and Statistical Inference | 9th Edition | ISBN: 9780321923271 | Authors: Robert V. Hogg, Elliot Tanis, Dale Zimmerman
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A certain machine has a life X that has an exponential

Chapter 3, Problem 15E

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QUESTION:

Problem 15E

A certain machine has a life X that has an exponential distribution with mean 10. The warranty is such that 100% of the price is returned if the machine fails in the first year, and 50% of the price is returned for a failure during the second year, and nothing is returned after that. If the machine cost $2500, what are the expected value and the standard deviation of the return on the warranty?

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QUESTION:

Problem 15E

A certain machine has a life X that has an exponential distribution with mean 10. The warranty is such that 100% of the price is returned if the machine fails in the first year, and 50% of the price is returned for a failure during the second year, and nothing is returned after that. If the machine cost $2500, what are the expected value and the standard deviation of the return on the warranty?

ANSWER:

Answer :

Step 1 of 3 :

Given,  

A machine has a life X.

Let X follows exponential distribution with mean 10. The warranty of the machine has given that 100% of the price is returned if the machine fails in first year and 50% of the price is returned if the machine fails in second year and nothing is returned after that.

The cost of the machine is $2500.

The claim is to find the expected value and the standard deviation of the return on the warranty.

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