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12. Let (X,) be a sequence of uncorrelated random variables (i.e., Cov(X;, X;) = 0 for i # j) with expectation 0 and variance 1.
12. Let (X,) be a sequence of uncorrelated random variables (i.e., Cov(X;, X;) = 0 for i # j) with expectation 0 and variance 1. Prove that for any bounded random variable Y, we have lim,-+ E[X,Y] = 0. Hint: With an := E[X,Y], first consider 2 BY -COX)
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