Be specific, do we have $$f_X(x)f_Y(y) \geq f_{X,Y}(x,y)?$$ It is very easy to find a counterexample in the discrete case. So under the continuous case, and under what assumptions will we have this inequality?
Many thanks for any comment.
2026-03-26 22:54:23.1774565663
Does the product of the marginal densities has some relation with the joint density?
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