# Probability insurance company problem

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1. Jul 31, 2016

### Mark53

1. The problem statement, all variables and given/known data
(4) (a) Let X be a random variable defined by the probability mass function P(X = x). The possible values X can take (denoted x) and the probability of those values occuring P(X = x) can be seen below

x 0 1000 2000 5000
P(X = x) 0.94 0.03 0.02 0.01

Find E(X).

(b) An insurance company offers extra insurance for car rentals to cover incidental damage, such as windscreens and tyres not covered by the primary insurance, and also the excess charged by the primary insurance in case of an accident. Let X be the amount paid out by the company on a randomly chosen policy of duration 10 days and suppose X follows the probability distribution in (a) above. If the premium charged for the policy is $180.00, what is the expected profit to the company for a single policy with a duration of 10 days? 3. The attempt at a solution a) E(x)=1000x0.003+2000x0.003+5000x0.01 E(x)=120 b) would this just be 180-120=$60

2. Jul 31, 2016

### TomHart

My last probability course was more than 30 years ago, but this problem seems pretty straight forward. Your answer has to be right. And I offer a money back guarantee if I am wrong.

3. Jul 31, 2016