A certain machine has a life X that has an exponential distribution with mean 10. The

Chapter 3, Problem 3.4-15

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QUESTION:

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:

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:

Step 1 of 3

Given:  has an exponential distribution with mean of

 is the return on the warranty. The machine costs  :  of the price is returned if the machine fails in the first year and  of the price is returned if the machine fails in the second year:

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