# Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

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## Uncorrelatedness sets for random variables with given distributionsHTML articles powered by AMS MathViewer

by Sofiya Ostrovska
Proc. Amer. Math. Soc. 133 (2005), 1239-1246 Request permission

## Abstract:

Let $\xi _1$ and $\xi _2$ be random variables having finite moments of all orders. The set $U(\xi _1,\xi _2):=\left \{(j,l)\in \textbf {N}^2:\textbf {E}\left (\xi _1^j\xi _2^l\right )=\textbf {E}\left (\xi _1^j\right )\textbf {E}\left ( \xi _2^l\right )\right \}$ is said to be an uncorrelatedness set of $\xi _1$ and $\xi _2.$ 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.
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• Sofiya Ostrovska
• Affiliation: Department of Mathematics, Atilim University, 06836 Incek, Ankara, Turkey
• MR Author ID: 329775
• Email: ostrovskasofiya@yahoo.com
• Received by editor(s): September 22, 2003
• Received by editor(s) in revised form: December 22, 2003
• Published electronically: October 18, 2004
• Communicated by: Richard C. Bradley