Assignment:
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:
| x ($ millions) |
P(x) |
| $1,700 |
0.2 |
| 1500 |
0.2 |
| 1200 |
0.3 |
| 1000 |
0.1 |
| 800 |
0.1 |
| 600 |
0.05 |
| 400 |
0.05 |
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.
Your answer must be typed, double-spaced, Times New Roman font (size 12), one-inch margins on all sides, APA format and also include references.