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. = =

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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B1. Let X₁ and Y; be random variables with Var(X;) = o² and Var(Y₂) o for all
ie {1,...,n}. Assume that each pair (X₁, Y;) has correlation Corr(X, Y) = p, but
that (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?
Transcribed Image Text:= B1. Let X₁ and Y; be random variables with Var(X;) = o² and Var(Y₂) o for all ie {1,...,n}. Assume that each pair (X₁, Y;) has correlation Corr(X, Y) = p, but that (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?
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