What is the expected profit for a car rental insurance company?

[Mark53]

Homework Statement

(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 occurring 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?

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

I am unsure about this part

 

[haruspex]

2000x0.003

Check that again.

would this just be

It would be, given the right number from a).

 

[Mark53]

Check that again.

It would be, given the right number from a).

Thanks