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Suppose X_i are iid with mean mu_x and variance X 2 < and Y_i are iid with mean mu_y and variance Y 2 < Let

Suppose X_i are iid with mean mu_x and variance X2< and Y_i are iid with mean mu_y and varianceY2< LetXn be the sample mean of the X_i and Ynbe the mean of Y_i. Find the limiting distribution, as min(m,n) of Z_n defined by

Zn=nX2+mY2[YmXn(YX)]

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