Question

[4C-04] An insurance policy reimburses a loss with a deductible of 5. That is, if a loss is less than 5, policy will pay zero. If it is more than 5, then the policy will pay (loss - 5). The policyholder's loss, Y, follows a distribution with density function: f(y) = 2y^-3 for 1 < y and 0 otherwise What is the expected value of the benefit paid under the insurance policy? (Use 2 decimals)

Answer 1

-3

Explanation:

Given that an insurance policy reimburses a loss with a deductible of 5. That is, if a loss is less than 5, policy will pay zero. If it is more than 5, then the policy will pay (loss - 5).

We have distribution of y as

`f(y) = (2)/(y^3) , y>1\\      =0 otherwise`

expected value of the benefit paid under the insurance policy

=
`E(Y-5)\\=E(Y)-5`, by linearity property of expectation.

`E(y) = \int\limits^\infty_1 {y((2)/(y^3) )} \, dy\\=(-2)/(y) \\=-0+2\\=2`

Hence expected value of the benefit paid under the insurance policy

=2-5 =-3