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# An insurance agent receives a bonus if the loss ratio L on

ISBN: 9780321923271 41

## Solution for problem 17E Chapter 3.1

Probability and Statistical Inference | 9th Edition

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Problem 17E

An insurance agent receives a bonus if the loss ratio L on his business is less than 0.5, where L is the total losses (say, X) divided by the total premiums (say, T). The bonus equals (0.5 − L)(T/30) if L < 0.5 and equals zero otherwise. If X (in \$100,000) has the pdf

and if T (in \$100,000) equals 3, determine the expected value of the bonus.

Step-by-Step Solution:

Step 1 of 1:

Given the loss ratio L on his business is less than 0.5.

Where L is the total losses divided by the total premiums.

Let B(x) = the bonus received given that the total losses was x.

Then since X=LT and T=3.

We have x = total losses, whose pdf is

Our goal is to find

The expected value of the bonus.

We have x = total losses, whose pdf is

We know that

B(x) = the bonus received given that the total losses was x.

Then since X=LT and T=3.

The formula for B(x) is given by,

Then...

Step 2 of 3

Step 3 of 3

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An insurance agent receives a bonus if the loss ratio L on

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