If the covariance of two random variables X and Y is positive,then Var(X - Y)will be larger than Var(X + Y).

Name: If the covariance of two random variables X and Y is positive,then Var(X - Y)will be larger than Var(X + Y).
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We know that Var(X-Y) = Var(X) + Var(Y) - 2Cov(X,Y) and Var(X+Y) = Var(X) + Var(Y) + 2Cov(X,Y)
Therefore, if Cov(X,Y) is positive, then Var(X-Y) = Var(X) + Var(Y) - 2Cov(X,Y) will be smaller than Var(X) + Var(Y) + 2Cov(X,Y) = Var(X+Y).

If the Covariance of Two Random Variables X and Y