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Problem 3. Let X and Y be the discrete random variables with the given pmf px (x₁) and py (yi). Assume E[X²] < ∞, E[Y²] < ∞. Variance and covariance are defined as Var (X) = E[(X - E[X])²], Cov(X, Y) = E[(X – E[X])(Y — E[Y])]. Verify that ● Var(X) = E[X²] – E[X]². • Cov(X, Y) = E[XY] – E[X]E[Y]. • Var(aX + c) = a²Var(X). • Var (X + Y) = Var(X) + Var(Y) + Cov(X, Y).

Problem 3. Let X and Y be the discrete random variables with the given pmf px (x₁) and py (yi). Assume E[X²] < ∞, E[Y²] < ∞. Variance and covariance are defined as Var (X) = E[(X - E[X])²], Cov(X, Y) = E[(X – E[X])(Y — E[Y])]. Verify that ● Var(X) = E[X²] – E[X]². • Cov(X, Y) = E[XY] – E[X]E[Y]. • Var(aX + c) = a²Var(X). • Var (X + Y) = Var(X) + Var(Y) + Cov(X, Y).

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 3. Let X and Y be the discrete random variables with the given pmf px (x₁) and py (yi). Assume E[X²] < ∞, E[Y²] < ∞. Variance and covariance are defined as Var (X) = E[(X - E[X])²], Cov(X, Y) = E[(X – E[X])(Y — E[Y])]. Verify that ● Var(X) = E[X²] – E[X]². • Cov(X, Y) = E[XY] – E[X]E[Y]. • Var(aX + c) = a²Var(X). • Var (X + Y) = Var(X) + Var(Y) + Cov(X, Y).
Transcribed Image Text:Problem 3. Let X and Y be the discrete random variables with the given pmf px (x₁) and py (yi). Assume E[X²] < ∞, E[Y²] < ∞. Variance and covariance are defined as Var (X) = E[(X - E[X])²], Cov(X, Y) = E[(X – E[X])(Y — E[Y])]. Verify that ● Var(X) = E[X²] – E[X]². • Cov(X, Y) = E[XY] – E[X]E[Y]. • Var(aX + c) = a²Var(X). • Var (X + Y) = Var(X) + Var(Y) + Cov(X, Y).
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