# 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.

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.

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