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Statistics / Probability and Statistical Inference 9 / Chapter 3.4 / Problem 16E

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

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QUESTION:

Problem 16E

A certain machine has a life X that has an exponential distribution with mean 10. The warranty is such that $m is returned if the machine fails in the first year, (0.5)m of the price is returned for a failure during the second year, and nothing is returned after that. If the machine cost $2500, find m so that the expected payment is $200.

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QUESTION:

Problem 16E

A certain machine has a life X that has an exponential distribution with mean 10. The warranty is such that $m is returned if the machine fails in the first year, (0.5)m of the price is returned for a failure during the second year, and nothing is returned after that. If the machine cost $2500, find m so that the expected payment is $200.

ANSWER:

Answer :

Step 1 of 2 :

Given, A machine has a life X.

Let X follows exponential distribution with mean 10. The warranty of the machine has given that m of the price is returned if the machine fails in first year and (0.5)m 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 and the expected payment $200.

The claim is to find the m value.

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