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arXiv · 1609.03004

Mean and Minimum of Independent Random Variables

Naomi Dvora Feldheim·Ohad Noy Feldheim
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Abstract

We show that any pair $X, Y$ of independent, non-compactly supported random variables on $[0,\infty)$ satisfies $\liminf_{m\to\infty} \mathbb{P}(\min(X,Y) >m \,| \,X+Y> 2m) =0$. We conjecture multi-variate and weighted generalizations of this result, and prove them under the additional assumption that the random variables are identically distributed.

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Naomi Dvora Feldheim, Ohad Noy Feldheim. 2016-09-10. Mean and Minimum of Independent Random Variables. https://arxiv.org/abs/1609.03004

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