Refer to problem 3–23. Find the variance and the standard deviation of hedge fund managers’ income.
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?
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