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where p(X,Y) denotes the correlation coefficient between random variables X and Y. Find expected value and variance of the random variable Z = X-0.5Y.

where p(X,Y) denotes the correlation coefficient between random variables X and Y. Find expected value and variance of the random variable Z = X-0.5Y.

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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**Problem 2** Random variables \( X \) and \( Y \) are such that \[ E(X) = 1, \quad E(Y) = -2, \] \[ \text{Var}(X) = 4, \quad \text{Var}(Y) = 16, \quad \rho(X, Y) = 0.5, \] where \( \rho(X, Y) \) denotes the correlation coefficient between random variables \( X \) and \( Y \). Find the expected value and variance of the random variable \( Z = X - 0.5Y \).
Transcribed Image Text:**Problem 2** Random variables \( X \) and \( Y \) are such that \[ E(X) = 1, \quad E(Y) = -2, \] \[ \text{Var}(X) = 4, \quad \text{Var}(Y) = 16, \quad \rho(X, Y) = 0.5, \] where \( \rho(X, Y) \) denotes the correlation coefficient between random variables \( X \) and \( Y \). Find the expected value and variance of the random variable \( Z = X - 0.5Y \).
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