Probability bounds for $n$ random events under $(n1)$wise independence
Abstract
A collection of $n$ random events is said to be $(n  1)$wise independent if any $n  1$ events among them are mutually independent. We characterise all probability measures with respect to which $n$ random events are $(n  1)$wise independent. We provide sharp upper and lower bounds on the probability that at least $k$ out of $n$ events with given marginal probabilities occur over these probability measures. The bounds are shown to be computable in polynomial time.
 Publication:

arXiv eprints
 Pub Date:
 November 2022
 DOI:
 10.48550/arXiv.2211.01596
 arXiv:
 arXiv:2211.01596
 Bibcode:
 2022arXiv221101596N
 Keywords:

 Mathematics  Probability;
 60E05
 EPrint:
 18 pages, 2 tables