A note on optimal probability lower bounds for centered random variables
Volume 113 / 2008
Colloquium Mathematicum 113 (2008), 231-240
MSC: Primary 60E15.
DOI: 10.4064/cm113-2-5
Abstract
We obtain lower bounds for ${\mathbb P}(\xi\geq 0)$ and ${\mathbb P}({\xi> 0})$ under assumptions on the moments of a centered random variable $\xi$. The estimates obtained are shown to be optimal and improve results from the literature. They are then applied to obtain probability lower bounds for second order Rademacher chaos.
