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