Refer to problem 3–7. Suppose that hedge funds must withhold $300 million 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 property of expected values are you using?

problem 3–7

An article in The New York Times reports that several hedge fund managers now make more than a billion dollars a year.2 Suppose that the annual income of a hedge fund manager in the top tier, in millions of dollars a year, is given by the following probability distribution:

a. Find the probability that the annual income of a hedge fund manager will be between $400 million and $1 billion (both inclusive).

b. Find the cumulative distribution function of X.

c. Use F(x) computed in (b) to evaluate the probability that the annual income of a hedge fund manager will be less than or equal to $1 billion.

d. Find the probability that the annual income of a hedge fund manager will be greater than $600 million and less than or equal to $1.5 billion