Do The Math Q15

Do The Math Q15

An auto insurance company insures an automobile worth 15,000 for one year under a policy with a 1,000 deductible. During the policy year there is a 0.04 chance of partial damage to the car and a 0.02 chance of a total loss of the car. If there is partial damage to the car, the amount X of damage (in thousands) follows a distribution with density function

What is the expected claim payment?

  1. 320
  2. 328 Correct Answer
  3. 352
  4. 380
  5. 540

Solution: B

Let Y denote the claim payment made by the insurance company.
Then

It follows that the expected claim payment is 328.