I have no idea on how to solve this assignment, so I'll try here again.

An article in The New York Times reports that several hedge fund managers now make more than a billion dollars a year. The annual income of a hedge fund manager in the top tier, in millions of dollars, is given by the following probability distribution.


Suppose the hedge funds must withhold $300 from the income of the manager, and an additional 5% of the remaining income. Find the expected net income of a manager in this group. What properties of expected values are you using?

The correct answer is $868,5 millions.

Ok..I started to minus $300 dollars from each manager, and then I removed the additional 5% of the remaining income.


But what do I do now? I think I am to use the expected value of a discreet random variable, which is equal to the sum of all the values of the random variable, each value multiplied by its probability
.
If I do this with the new numbers, I get $883,5. What am I doing wrong? :(