A probabilistic inequality for sums of bounded symmetric independent random variables

Abstract

An inequality ∫x x+2 P{|∑i=1 n ξi| ≥ t} dt ≤ ∫x x+2 P{|∑i=1 n εi| ≥ t} dt is proved which describes an extremal property of a two-point distribution within the class of symmetric distributions with bounded support. © 1997 Plenum Publishing Corporation.