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[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)

Respuesta :

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

[tex]f(y) = \frac{2}{y^3} , y>1\\      =0 otherwise[/tex]

expected value of the benefit paid under the insurance policy

=[tex]E(Y-5)\\=E(Y)-5[/tex], by linearity property of expectation.

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

Hence expected value of the benefit paid under the insurance policy

=2-5 =-3

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