A one-sided probability inequality for the sum of independent, bounded random variables

Abstract

This paper shows that if x 1 ,x 2 , …, x n are n totally independent random variables, not necessarily identically distributed, with var(x i ) ≤ 2 i , bounded above so that x i E(x i ) ≤ M i , and if S= σx i , then P { S E(S) ≥ k σ M i } is less than or equal to an explicit function of k(k< 1), r= min(M i / i B = σM i / max(M i ). A table is provided which allows easy calculation of the numerical value of the inequality.