Convolution Inequalities with Probability Distributions

Abstract

There are many results related to inequalities linked to convolutions. We can create a new probability distribution from well-known probability distributions. One of the classical method is addition. If we want to find the probability distribution of the sum of two independent probability random variables then we need to find the convolution of their distributions. In this paper, I computed the upper bound of the convolution of several several independent random variables: Normal Distributions and Exponential Distributions.