Moments of a random variable arising Laplacian random variable

TL;DR

This paper explicitly derives the moments of the Laplacian random variable with specific parameters, expressing them through Bernoulli and Euler numbers, providing a clear mathematical characterization.

Contribution

It introduces explicit formulas for the moments of the Laplacian distribution using Bernoulli and Euler numbers, which was not previously detailed.

Findings

Explicit formulas for moments in terms of Bernoulli and Euler numbers

Mathematical characterization of Laplacian moments

Enhanced understanding of Laplacian distribution properties

Abstract

Let X be the Laplacian random variable with parameters (a,b)=(0,1), and let X1, X2, X3 , ...be a sequence of mutually independent copies of X$. In this note, we explicitly determine the moments of the Laplacian random variable in terms of the Bernoulli and Euler numbers.