PS 5 full - ECON 2843 Problem Set 5 1. Problem 6.1 in...

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ECON 2843 Problem Set 5 1. Problem 6.1 in Newbold on p. 183 An analyst has available two forecasts, F 1 and F 2 , of earnings per share of a corporation next year. He intends to form a compromise forecast as a weighted average of the two individual forecasts. In forming the compromise forecast, weight X will be given to the first forecast and weight (1 – X) to the second, so that the compromise forecast is X F 1 + (1 – X) F 2 . The analyst wants to choose a value between 0 and 1 for the weight X, but he is quite uncertain of what will be the best choice. Suppose that what eventually emerges as the best possible choice of the weight X can be viewed as a random variable uniformly distributed between 0 and 1, having probability density function: f(x) = 1 for 0 ≤ x ≤ 1 0 for all other values of x a. Draw the probability density function. b. Find and draw the cumulative distribution function. c. Find the probability that the best choice of the weight X is less than .25. d. Find the probability that the best choice of the weight X is more than .75. e. Find the probability that the best choice of the weight X is between .2 and .8. 2. Problem 6.7 in Newbold on p. 186. A charitable organization solicits donations by telephone. Employees are paid \$60 plus 20 % of the money their calls generate each week. The amount of money generated n a week can be viewed as a random variable with mean \$700 and standard deviation \$130. Find the mean and standard deviation of an employee’s total pay in a week. 3. Problem 6.9 in Newbold on p. 197. Let the random variable Z follow a standard normal distribution. a.

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This note was uploaded on 04/07/2008 for the course ECON 2843 taught by Professor Hudgins during the Spring '08 term at The University of Oklahoma.

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PS 5 full - ECON 2843 Problem Set 5 1. Problem 6.1 in...

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