Approximation of Expected Values of Non-Linear Functions of Random Variables

Abstract

In this thesis, we discussed some new bounds and approximations of the expected values of certain nonlinear functions of a random variable X. We discussed several methods to compute the approximated values, the upper bounds and the lower bounds of E[(X+ c)^d],c ≥ 0,d < 0 and E[1/(X+c) ^[n]], c ≥ 0, n = 1,2,…. The methods discussed have simple computations and often give improved results.