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# Let X be the damage incurred (in \$) in a certain type of ISBN: 9780321629111 32

## Solution for problem 36E Chapter 3

Probability and Statistics for Engineers and the Scientists | 9th Edition

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Problem 36E

Let X be the damage incurred (in \$) in a certain type of accident during a given year. Possible X values are 0, 1000, 5000, and 10000, with probabilities .8, .1, .08, and .02, respectively. A particular company offers a \$500 deductible policy. If the company wishes its expected profit to be \$100, what premium amount should it charge?

Step-by-Step Solution:

Answer Step 1 of 3 Let x=The damage incurred y=premium should charge g=The cost to insurance company Then g(x)=x-500 y(x)=E(g(x))+100 P(x)= probability assigned Step 2 of 3 x P(x) g(x)=x-500 y(x) 0 0.8 0 100 1000 0.1 500 600 5000 0.08 4500 4600 10000 0.02 9500 9600

Step 3 of 3

##### ISBN: 9780321629111

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