Some inequalities for probability, expectation, and variance of random variables defined over a finite interval

Abstract

The inequalities for cumulative distribution functions, expectation, variance, and applications were presented. The elementary inequalities linking the expectation and variance of a random variable were also considered. It was found that the Matic-Pecaric-Ujevic result provides a better bound for the first membership in terms of Euclidean norms using the Chebychev's functional.