Question: 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.