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

Answer:

-3

Step-by-step 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

$f(y) = \frac{2}{y^3} , y>1\\ =0 otherwise$

expected value of the benefit paid under the insurance policy

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

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

Hence expected value of the benefit paid under the insurance policy

=2-5 =-3