Title

An optimal upper bound on the tail probability for sums of random variables

Document Type

Article

Publication Date

10-22-2019

Department

Department of Mathematical Sciences

Abstract

Let $s$ be any given real number. An explicit construction is provided of random variables (r.v.'s) $X$ and $Y$ such that $\sup{P}(X+Y\ge s)$ is attained, where the $\sup$ is taken over all r.v.'s $X$ and $Y$ with given distributions.

Publication Title

Theory of Probability & Its Applications

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