A customer buys a $1000 deductible policy on her $31,000 car. The probability of having an accident in which the loss is greater than $1000 is 0.03, and then that loss, as a fraction of the value of the car minus the deductible, has the pdf f(x) = 6(1 − x)5, 0 < x < 1.
(a) What is the probability that the insurance company must pay the customer more than $2000?
(b) What does the company expect to pay?