Pairwise Independent Random Variables

O'Brien, G. L.

Ann. Probab., Tome 8 (1980) no. 6, p. 170-175 / Harvested from Project Euclid

Résumé

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.

Détail

Publié le : 1980-02-14
Classification:  Pairwise independence,  stationary sequences,  pseudorandom numbers,  block designs,  60C05,  65C10,  60B99,  62K10