Suppose that you own a store that sells a particular stove for $1,000. You purchase the stoves from the distributor for $800 eac
h. You believe that this stove has a lifetime which can be faithfully modeled as an exponential random variable with a parameter of lambda = 1/10, where the units of time are years. You would like to offer the following extended warranty on this stove: if the stove breaks within r years, you will replace the stove completely (at a cost of $800 to you). If the stove lasts longer than r years, the extended warranty pays nothing. Let $C be the cost you will charge the consumer for this extended warranty. For what pairs of numbers (C,r) will the expected profit you get from this warranty be zero. What do you think are reasonable choices for C and r? Why?
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