(L&K 4.9) Suppose X is a discrete random variable with px(x) = 0.25 for x = -2, -1, 1, 2. Let Y also be a discrete random variable such that Y = X2. Show that Cov(X,Y)= 0. Therefore, uncorrelated random variables are not necessarily independent.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 22E
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(L&K 4.9) Suppose X is a discrete random variable with px(x) = 0.25 for x = -2, -1, 1, 2. Let Y also
be a discrete random variable such that Y = X2. Show that Cov(X,Y)= 0. Therefore, uncorrelated
random variables are not necessarily independent.
Transcribed Image Text:(L&K 4.9) Suppose X is a discrete random variable with px(x) = 0.25 for x = -2, -1, 1, 2. Let Y also be a discrete random variable such that Y = X2. Show that Cov(X,Y)= 0. Therefore, uncorrelated random variables are not necessarily independent.
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