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When car has a lifetime distribution exp(1/4), the owner wants to change the car either it is broken or the car is 8 years old.

When car has a lifetime distribution exp(1/4), the owner wants to change the car either it is broken or the car is 8 years old. If it is replaced at 8 years (not broken), the owner pays 20, 000 dollars. If it is broken, the owner spends in total 25, 000 dollars. What is the long-term expected cost per unit time?

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