(Warranty). A warranty is written on a product worth $10,000 so that the buyer is given $8000 if

it fails in the first year, $6000 if it fails in the second, $4000 if it fails in third, $2000 if it fails in

the fourth, and zero after that. Its probability of failing in a year is 0.1; failures are independent

of those of other years. What is the expected value of the warranty? Also find the variance?