Let X and Y be two random variables with means 1 and 3 and variances 3 and 7, respectively. Consider the random variable W that is a weighted average of X and Y, given by W = aX+(1-a)Y, where a = 0.37. Answer the following, rounding your answers to two decimal places. (a) What is the mean of 2W? b) Assume that X and Y are independent. What is the variance of 2W? (c) Now assume that Cov(X,Y) = −1.7. What is the variance of 2W?

Let X and Y be two random variables with means 1 and 3 and variances 3 and 7, respectively. Consider the random variable W that is a weighted average of X and Y, given by W = aX+(1-a)Y, where a = 0.37. Answer the following, rounding your answers to two decimal places. (a) What is the mean of 2W? b) Assume that X and Y are independent. What is the variance of 2W? (c) Now assume that Cov(X,Y) = −1.7. What is the variance of 2W?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

Let X and Y be two random variables with means 1 and 3 and variances 3 and 7, respectively. Consider the random variable W that is a weighted average of X and Y, given by

W = aX+(1-a)Y,

where a = 0.37. Answer the following, rounding your answers to two decimal places.

(a) What is the mean of 2W?

b) Assume that X and Y are independent. What is the variance of 2W?
(c) Now assume that Cov(X,Y) = −1.7. What is the variance of 2W?

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