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suppose (X 1 ,Y 1 )... (X_n, Y_n) are i.i.d bivariate random vectors such that X_i and Y_i have finite nonzero variances. Then , the

suppose (X1,Y1)... (X_n, Y_n) are i.i.d bivariate random vectors such that X_i and Y_i have finite nonzero variances. Then , the correlation =(Xi,Yi)is well defined. Let XnandYnbe the sample means of Xs and Ys, respectively. Let n^be the sample correlation defined by

n^=i=1n(XiXn)2(YiYn)2i=1n(XiXn)(YiYn)

argue thatn^p

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