11.65. Suppose you buy an electronic device that you operate continuously. The device costs you $300 and carries a one-year warranty. The warranty states that if the device fails during its first year of use, you get a new device for no cost, and this new device carries exactly the same warranty, i.e., if it fails within a year after to receive it, you a new device for no cost. However, if it fails after the first year of use, the warranty is of no value.

You plan to use this device for the next six years. Therefore, any time the device fails outside its warranty period, you will pay $300 for another device of the same kind. (We assume the price does not increase during the six-year period.) The time until failure for a device is gamma distributed with parameters = 2 and = 0.5. (This implies a mean time to failure of one year.) Use @RISK to simulate the six-year period. Use simulation with 10,000 iterations to answer the questions.

a. What is the expected total cost of ownership during the six-year period, which is the sum of the initial purchase cost and replacement costs (outside of warranty) during the six years. The expected cost is?

b. What is the expected number of devices owned during the six-year period (i.e., initial device plus total number of replacements)? The expected number of devices owned is?