Find the cumulative distribution function of x

Reference no: EM131370733

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.

Reference no: EM131370733

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