Abstract:  Literature [1]obtained an upper bound inequality for the variance of a function of a standard normal random variable,using Hermite polynomials.In this paper we extend and im- prove the result of [1]and obtain an upper bound inequality for the rth absolute moment of a function of a random variable and an upper bound for the variance of a random variable function is also given.

Key words: function , of , a , random , variable, variance, inequality ,  , of , rth , absolute , moment