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Uncorrelatedness sets for random variables with given distributions

Authors:	Sofiya Ostrovska

Affiliation:	Department of Mathematics, Atilim University, 06836 Incek, Ankara, Turkey

Abstract:	Let and be random variables having finite moments of all orders. The set $begin{displaymath}U(xi_1,xi_2):=left{(j,l)in {bf N}^2:{bf E}left(xi_1^... ...{bf E}left(xi_1^jright){bf E}left( xi_2^lright)right}end{displaymath}$ is said to be an uncorrelatedness set of and It is known that in general, an uncorrelatedness set can be arbitrary. Simple examples show that this is not true for random variables with given distributions. In this paper we present a wide class of probability distributions such that there exist random variables with given distributions from the class having a prescribed uncorrelatedness set. Besides, we discuss the sharpness of the obtained result.

Keywords:	Uncorrelatedness independence uncorrelatedness set quasianalytic class characteristic function

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