Chapter 3.2, Problem 20E

The initial value of an appliance is $700 and its dollar value in the future is given by $v\left(t\right)=100\left(2^{3-t}-1\right),0\le t\le 3,$

where (is time in years. Thus, after the first three years. the appliance is worth nothing as far as the warranty is Concerned. If it fails in the first three years, the warranty pays v(t). Compute the expected value of the payment on the warranty if T has an exponential distribution with mean 5.