Question: Let X1, X2, , Xn be i.i.d. random variables with mean and variance 2 , and let X_bar = (X1 + X2 + + Xn)/

Let X1, X2, , Xn be i.i.d. random variables with mean and variance 2 , and let X_bar = (X1 + X2 + + Xn)/ n be the sample mean. Show that for any i, Xi X_bar and X_bar are uncorrelated.

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