Uncorrelatedness Sets of Discrete Random Variables Via Vandermonde-Type Determinants

Abstract

Given random variables X and Y having finite moments of all orders, their uncorrelatedness set is defined as the set of all pairs (j, k) is an element of N-2; for which X-j and Y-kappa are uncorrelated. It is known that, broadly put, any subset of N-2 can serve as an uncorrelatedness set. This claim is no longer valid for random variables with prescribed distributions, in which case the need arises so as to identify the possible uncorrelatedness sets. This paper studies the uncorrelatedness sets for positive random variables uniformly distributed on three points. Some general features of these sets are derived. Two related Vandermonde-type determinants are examined and applied to describe uncorrelatedness sets in some special cases. (C) 2019 Mathematical Institute Slovak Academy of Sciences