Let x1, ,Xn be uncorrelated, each with variance 2 Let Y1, , Yn be positively correlated, each with variance 2 Prove that the variance of X is smaller than the variance of Y

Question: Let x1, . . . ,Xn be uncorrelated, each with variance 2. Let Y1, . . . , Yn be positively correlated, each with variance

Let x1, . . . ,Xn be uncorrelated, each with variance σ2. Let Y1, . . . , Yn be positively correlated, each with variance σ2. Prove that the variance of X is smaller than the variance of Y .

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