Question: Show that if X and Y have the same distribution, then: VAR(X + Y / 2) VAR ( X ) and conclude that the use

Show that if X and Y have the same distribution, then: VAR(X+Y / 2) VAR (X)

and conclude that the use of antithetical variables can never increase variance (Inequality Cauchy-Schwarz:

E (XY) E (X2) E(Y2) | E(XY) E(X2)

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