## Uncorrelatedness sets for random variables with given distributions

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- by Sofiya Ostrovska
- Proc. Amer. Math. Soc.
**133**(2005), 1239-1246 - DOI: https://doi.org/10.1090/S0002-9939-04-07698-1
- Published electronically: October 18, 2004
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## 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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## Bibliographic Information

**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
- © Copyright 2004
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc.
**133**(2005), 1239-1246 - MSC (2000): Primary 60E05
- DOI: https://doi.org/10.1090/S0002-9939-04-07698-1
- MathSciNet review: 2117227