=B1. Let X₁ and Y; be random variables with Var(X;) = o² and Var(Y₂) o for allie {1,...,n}. Assume that each pair (X₁, Y;) has correlation Corr(X, Y) = p, butthat (X₁, Y₂) and (X₁, Y;) are independent for all i j.(a) What is Cov(X₁, Yi) in terms of Ox, Oy(b) Show that Cov(X₁,Y) = poxoy/n, where Y is the average of the Y₁.(c) Determine Cov(X, Y).and p?

(a) The covariance between Xi and Yi is given by: Cov(Xi, Yi) = E[(Xi - E[Xi])(Yi - E[Yi])] Since…

Answered: Let X and Y be random variables with…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section: Chapter Questions

Problem 52RE

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EXER 6.3 Find the covariance and the correlation coefficient between X and Y, if X and Y are jointly discrete random variables, with joint PMF given by: SHOW SOLUTIONS X\Y 0 1 6 0 28 6 1 28 2 0 333333 28 28 28 2120 28 0
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Let X and Y be random variables with Var (X₂) o and Var(Y₂) o for all ie {1,...,n}. Assume that each pair (X₁, Yi) has correlation Corr(X₁, Y) = p, but that (X₁, Y₂) and (X, Y,) are independent for all i j. = =