Notes on Two Inequalities for Random Variables Whose Probability Density Functions Are Bounded (Report‪)‬

1. Introduction In a previous paper (4), Hwang using an improvement of Gruss inequality to establish some inequalities for expectation and the distribution function in order to improve the corresponding inequalities established by Barnett and Dragomir in (1) or (2) by using the pre-Gruss inequality. It is a pity that there exist some errors in two main theorems (see Theorem 7 and Theorem 9 of (4)). The purpose of this paper is to provide a corrected version of these two theorems.