feral

July 18th 2008, 10:29 AM

So...I understand most of how this problem is setup, but there is one part I can't wrap my understanding around:

An auto insurance company insures an automobile worth 13,000 for one year under a policy with a 1,000 deductible. During the policy year there is a 0.08 chance of partial damage to the car and a 0.04 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

f(x)={0.2601e-x4 for 0<x<13 otherwise

What is the expected claim payment.

Answer:

Y is my claim payment and its distributed

Max (0, x-1) for p=.08

12 for p=.04

0 p=.88

.88 (0) + .08 (.2601) (integral of density function * (x-1)) + (.04)(12).

Can someone explain to me why .04 is multiplied by 12? I know you need to include this .04 since we are dealing with the expected claim payment, but why 12?

An auto insurance company insures an automobile worth 13,000 for one year under a policy with a 1,000 deductible. During the policy year there is a 0.08 chance of partial damage to the car and a 0.04 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

f(x)={0.2601e-x4 for 0<x<13 otherwise

What is the expected claim payment.

Answer:

Y is my claim payment and its distributed

Max (0, x-1) for p=.08

12 for p=.04

0 p=.88

.88 (0) + .08 (.2601) (integral of density function * (x-1)) + (.04)(12).

Can someone explain to me why .04 is multiplied by 12? I know you need to include this .04 since we are dealing with the expected claim payment, but why 12?