Probability bounds for $n$ random events under $(n-1)$-wise independence

Karthik Natarajan; Arjun Kodagehalli Ramachandra; Colin Tan

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arXiv · 2211.01596

Probability bounds for $n$ random events under $(n-1)$-wise independence

Karthik Natarajan·Arjun Kodagehalli Ramachandra·Colin Tan

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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.

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Karthik Natarajan, Arjun Kodagehalli Ramachandra, Colin Tan. 2022-11-03. Probability bounds for $n$ random events under $(n-1)$-wise independence. https://arxiv.org/abs/2211.01596

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