Approximation of exponential functions of random variables by statistical linearization

The approximation of a nonlinear function of a random variable by a linear function is considered. An exponential function, which arises in problems such as random sampling and random parameter linear systems, is treated in detail. The values of the two parameters which define the linear function are given for various approximation criteria. The results are then applied to the Gaussian random variable case, with explicit results and numerical comparisons.