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NOTES ON A QUESTION OF UNCORRELATEDNESS AND DEPENDENCE

Cai Jun (Department of Mathematics)  
Given two-dimesnsional distribution functions F,G, we give a sufficient and necessary condition for the existence of two random veclors X=(X_1, X_2) and Y=(Y_1,Y_2),where X and Y has distribution F and Grespectively, X_i and Y_j(i,j=1, 2) are uncorrelated and not independent. In two-dimesnional case, we solve a question of uncorrelatedness and dependence of components of two random vectors. Also we give a necessary condition for general case of the question.
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