(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.
(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.
A First Course in Probability (10th Edition)
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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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb24639c0-4a5e-42d3-8ac2-dd222243bdd4%2F2d72ea2a-2e55-4654-9b8b-d9ba113f4620%2Fvqmakc8_processed.png&w=3840&q=75)
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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