A note on sub-independent random variables and a class of bivariate mixtures

摘要

First, we recall a concept which is called sub-independence. This concept is stronger than that of uncorrelatedness but a lot weaker than independence. The concept of sub-independence, unlike that of uncorrelatedness, does not depend on the existence of any moments. Then, we consider a particular bivariate mixture to construct a pair (X, Y), which is sub-independent but not independent.