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February, 1980 Pairwise Independent Random Variables
G. L. O'Brien
Ann. Probab. 8(1): 170-175 (February, 1980). DOI: 10.1214/aop/1176994834

Abstract

Let $Y_1, \cdots, Y_r$ be independent random variables, each uniformly distributed on $\mathscr{M} = \{1,2, \cdots, M\}$. It is shown that at most $N = 1 + M + \cdots + M^{r-1}$ pairwise independent random variables, all uniform on $\mathscr{M}$ and all functions of $(Y_1, \cdots, Y_r)$, can be defined. If $M = p^k$ for some prime $p$, the maximum can be attained by a strictly stationary sequence $X_1, \cdots, X_N$, for which any $r$ successive random variables are independent.

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G. L. O'Brien. "Pairwise Independent Random Variables." Ann. Probab. 8 (1) 170 - 175, February, 1980. https://doi.org/10.1214/aop/1176994834

Information

Published: February, 1980
First available in Project Euclid: 19 April 2007

zbMATH: 0426.60011
MathSciNet: MR556424
Digital Object Identifier: 10.1214/aop/1176994834

Subjects:
Primary: 60C05
Secondary: 60B99, 62K10, 65C10

Rights: Copyright © 1980 Institute of Mathematical Statistics

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Vol.8 • No. 1 • February, 1980
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