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 the third, $2000 if it fails in the fourth, and zero after that. The probability of the product's failing in a year is 0.1; failures are independent of those of other years. What is the expected value of the warranty?
I'm a bit confused as to how to solve this problem. At first I thought I'd simply multiply the possible warrantpayments with 0.1 and add it together, but this answer is incorrect. Any help in solving this would be greatly appreciated!