Sankhya: The Indian Journal of Statistics

2000, Volume 62, Series A, Pt. 3, pp.318--330

ON BERNSTEIN'S EXAMPLE OF THREE PAIRWISE INDEPENDENT RANDOM VARIABLES

By

YVES DERRIENNIC, Université de Bretagne Occidentale, Brest, France

and

ANDRZEJ KLOPOTOWSKI, Universitée Paris XIII, Institut Galilé, Villetaneuse, France

SUMMARY. We give here a complete description of triplets and quadruplets of pairwise independent binary random variables with a special emphasis on the role of Bernstein's example.

AMS (1991) subject classification. Primary 60A05, 60G10; secondary 47A35, 28D20.

Key words and phrases. Pairwise independence, one-dependence, stationarity, exchan\-geabi\-lity, Markov chain.

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