i.i.d. some distribution with mean 1 and finite variance. Let Y1, Y2, ... i.i.d. Let X1, X2, ... some other distribution with mean 2 and finite variance. Suppose the X;'s and the Y;'s are independent with each other. Prove that X1 + X2 + •…+ X, P,! as n → o Y1 + Y2 + · · · + Yn Does the above still hold if the X;'s and the Y;'s are not independent with each other? Explain. (We assume the X;'s themselves are still i.i.d. and the Y;'s themselves are still i.i.d.)

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