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(a) Draw the probability density function.

(a) Draw the probability density function.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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4. An analyst has available two forecasts, F₁ and F2, of earnings per share of a corporation next year. He intends to form a combined forecast as a weighted average of the two individual forecasts. In forming the combined forecast, weight X will be given to the first forecast and weight (1 - X) to the second, so that the combined forecast is XF₁+(1-X)F₂. 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 fx(x) = 1 for 0 < x < 1, and = 0 for all other values x of the random variable X. (a) Draw the probability density function. 1 (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 0.2 and 0.8. 5. An author receives a contract from a publisher, according to which she is to be paid a fixed sum of $50,000, plus $5.00 for each copy of her book sold. Her uncertainty about total sales of the book can be represented by a random variable with mean 30,000 and standard deviation 8,000. Find the mean and the standard deviation of the total payments she will receive.
Transcribed Image Text:4. An analyst has available two forecasts, F₁ and F2, of earnings per share of a corporation next year. He intends to form a combined forecast as a weighted average of the two individual forecasts. In forming the combined forecast, weight X will be given to the first forecast and weight (1 - X) to the second, so that the combined forecast is XF₁+(1-X)F₂. 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 fx(x) = 1 for 0 < x < 1, and = 0 for all other values x of the random variable X. (a) Draw the probability density function. 1 (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 0.2 and 0.8. 5. An author receives a contract from a publisher, according to which she is to be paid a fixed sum of $50,000, plus $5.00 for each copy of her book sold. Her uncertainty about total sales of the book can be represented by a random variable with mean 30,000 and standard deviation 8,000. Find the mean and the standard deviation of the total payments she will receive.
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