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.