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arXiv · 1407.0839

An Exponential Inequality for Symmetric Random Variables

Raphaël Cerf·Matthias Gorny
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Abstract

We prove the following exponential inequality: Let $n\geq 1$ and let $X_1,...,X_n$ be $n$ independent identically distributed symmetric real-valued random variables. For any $x,y>0$, we have \[\mathbb{P}\big({X_1+...+X_n}\geq x,\, {X_1^2+...+X_n^2}\leq y\big)< \exp(-\frac{x^2}{2y})\,.\]

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BibTeXRIS

Raphaël Cerf, Matthias Gorny. 2014-10-20. An Exponential Inequality for Symmetric Random Variables. https://arxiv.org/abs/1407.0839

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