Refer to problem 1. Find the variance and the standard deviation of hedge fund managers' income.
Problem 1
Refer to problem 2. Suppose that hedge funds must withhold $300 million from the income of the manager and an additional 5% of the remaining income. Find the expected net income of a manager in this group. What property of expected values are you using?
Problem 2
An article in The New York Times reports that several hedge fund managers now make more than a billion dollars a year. Suppose that the annual income of a hedge fund manager in the top tier, in millions of dollars a year, is given by the following probability distribution:
|
x($ millions)
|
P(x)
|
|
$1,700
|
0.2
|
|
1,500
|
0.2
|
|
1,200
|
0.3
|
|
1,000
|
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.