On probabilistic mean value theorem and covariance identities

Abstract

In this paper, further results for a probabilistic analogue of the mean value theorem proposed by Di Crescenzo (1999) are studied, focused on Normal and Poisson distributions. By applying this theorem for two normally distributed random variables with the same variance, a new symmetric unimodal distribution is obtained, and statistical measures of it are provided. By introducing a family of real valued continuous distributions, covariance identities are also investigated. Covariance identities are also explored for a Poisson distributed random variable. Some illustrative examples are finally given.