Some inequalities associated with the probability density function

Year 2025, Volume: 1 Issue: 1, 41 - 49, 28.11.2025

Mehmet Zeki Sarikaya

Abstract

In this paper, we establish improved versions of certain inequalities for random variables whose probability density functions are bounded and whose absolute derivatives are convex on the real line. The results obtained here serve as significant extensions and generalizations of previously known inequalities in the literature.

Keywords

Hermite-Hadamard inequality , trapezoid inequality , convex function , Hölder inequality , variance , Cebysev inequality

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