# Question: An analyst has available two forecasts F1 and F2 of

An analyst has available two forecasts, F1 and F2, 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 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 the probability density function

a. Graph the probability density function.

b. Find and graph the cumulative distribution function.

c. Find the probability that the best choice of the weight X is less than 0.25.

d. Find the probability that the best choice of the weight X is more than 0.75.

e. Find the probability that the best choice of the weight X is between 0.2 and 0.8.

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 the probability density function

a. Graph the probability density function.

b. Find and graph the cumulative distribution function.

c. Find the probability that the best choice of the weight X is less than 0.25.

d. Find the probability that the best choice of the weight X is more than 0.75.

e. Find the probability that the best choice of the weight X is between 0.2 and 0.8.

**View Solution:**## Answer to relevant Questions

Given an arrival process with l = 1.0, what is the probability that an arrival occurs in the first t = 2 time units? A professor sees students during regular office hours. Time spent with students follows an exponential distribution with a mean of 10 minutes. a. Find the probability that a given student spends fewer than 20 minutes with ...A random variable X is normally distributed with a mean of 100 and a variance of 100, and a random variable Y is normally distributed with a mean of 200 and a variance of 400. The random variables have a correlation ...Five inspectors are employed to check the quality of components produced on an assembly line. For each inspector the number of components that can be checked in a shift can be represented by a random variable with mean 120 ...The random variable X has probability density function as follows: a. Graph the probability density function for X. b. Show that the density has the properties of a proper probability density function. c. Find the ...Post your question