GENERATING NEW INEQUALITIES AND EQUALITIES: A STATISTICAL APPROACH

Wafik Youssef Younan (Egypt)

Received September 19, 2007

Abstract

This article gives a set of inequalities based on using known elementary inequalities and probability distributions. The concept depends on replacing the arguments in an elementary inequality with random variables whose domain must be consistent with the constraints the arguments obey. Taking the expectation of both sides of the inequality – after replacement – leads to the result. Seven probability distributions will be used with many elementary inequalities to generate inequalities. The same approach is used to generate a set of equalities too.

Keywords and phrases: elementary inequalities, probability distributions, mathematical expectation.