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Consider two random variables X and Y. Let c' be a deterministic constant. derive a simple expression for cov(X, cY) in terms of e and cov(X, Y). derive a simple expression for cov(X, X+Y) in terms of var(X) and cov(X,Y). Suppose the new random variables W=X and Z-X+aY. where 'a' is a deterministic constant. Find the value of 'a' according the stochastie parameters of X and Y so tha W and Z are uncorrelated.

Consider two random variables X and Y. Let c' be a deterministic constant. derive a simple expression for cov(X, cY) in terms of e and cov(X, Y). derive a simple expression for cov(X, X+Y) in terms of var(X) and cov(X,Y). Suppose the new random variables W=X and Z-X+aY. where 'a' is a deterministic constant. Find the value of 'a' according the stochastie parameters of X and Y so tha W and Z are uncorrelated.

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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2. Consider two random variables X and Y. Let 'e' be a deterministic constant. A) derive a simple expression for cov(X, cY) in terms of e and cov(X, Y). B) derive a simple expression for cov(X, X+Y) in terms of var(X) and cov(X,Y). C) Suppose the new random variables W=X and Z-X+aY. where 'a' is a deterministic constant. Find the value of 'a' according the stochastic parameters of X and Y so tha W and Z are uncorrelated.
Transcribed Image Text:2. Consider two random variables X and Y. Let 'e' be a deterministic constant. A) derive a simple expression for cov(X, cY) in terms of e and cov(X, Y). B) derive a simple expression for cov(X, X+Y) in terms of var(X) and cov(X,Y). C) Suppose the new random variables W=X and Z-X+aY. where 'a' is a deterministic constant. Find the value of 'a' according the stochastic parameters of X and Y so tha W and Z are uncorrelated.
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