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Q1: Variance, Covariance and Correlation for Univariate Random Variables Q1.1 If we have a set of N independent random variables, X₁, X₂,..., Xy, with E[X₂] = μ₁ and V[X₂] = o?. Please calculate the variance of their product, V[IIN_₁X;] in terms of μ; and ₁. Your Solution: Q1.2 Prove that -1 ≤ p(X,Y) ≤ 1 for two univariate random variables X and Y.

Q1: Variance, Covariance and Correlation for Univariate Random Variables Q1.1 If we have a set of N independent random variables, X₁, X₂,..., Xy, with E[X₂] = μ₁ and V[X₂] = o?. Please calculate the variance of their product, V[IIN_₁X;] in terms of μ; and ₁. Your Solution: Q1.2 Prove that -1 ≤ p(X,Y) ≤ 1 for two univariate random variables X and 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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Q1: Variance, Covariance and Correlation for Univariate Random Variables Q1.1 If we have a set of N independent random variables, X₁, X2, ..., XN, with E[X₂] = μ; and V[X₂] = o?. Please calculate the variance of their product, V[IINX;] in terms of u, and σ₁. Your Solution: Q1.2 Prove that -1 ≤ p(X,Y) ≤ 1 for two univariate random variables X and Y. Your Solution:
Transcribed Image Text:Q1: Variance, Covariance and Correlation for Univariate Random Variables Q1.1 If we have a set of N independent random variables, X₁, X2, ..., XN, with E[X₂] = μ; and V[X₂] = o?. Please calculate the variance of their product, V[IINX;] in terms of u, and σ₁. Your Solution: Q1.2 Prove that -1 ≤ p(X,Y) ≤ 1 for two univariate random variables X and Y. Your Solution:
▾ Q1.3: Show that if Y = ax + b for some a > 0 and b, then p(X,Y) = 1. Your Solution: + Code Your Solution: + Text Q1.4 Let X~ U(-1,1) and Y = X². Clearly Y is dependent on X. In fact, Y is uniquely determined by X. Show that p(X, Y) = 0. This gives an example that uncorrelated does not imply independent. ↑
Transcribed Image Text:▾ Q1.3: Show that if Y = ax + b for some a > 0 and b, then p(X,Y) = 1. Your Solution: + Code Your Solution: + Text Q1.4 Let X~ U(-1,1) and Y = X². Clearly Y is dependent on X. In fact, Y is uniquely determined by X. Show that p(X, Y) = 0. This gives an example that uncorrelated does not imply independent. ↑
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