When the functions of the random variables are complicated then the evaluation of the mean and the variance is difficult. In that case the function may be expanded using Taylor series expansion and the expectations are applied, may be on the first few terms of the expansion, to know the mean and variance. The expansion of the complicated function is carried about the mean of the random variable X. H(X) is expanded about the mean and the first three terms are given below;

Where Hⁿ (µ) is the n^th derivative of H(X) evaluated at µ.

By applying the expectation on the above function;

Since the H (µ), , and are constants, and is the variance of the random variable X the above equation results in the following form;

Then if the function of the random variable is H(X) the mean can be approximated using the following expression;

Similarly from the first two terms of the Taylor series expansion the variance of H(X) can be approximated with the following expression.

If the variance is large and the mean is small then it may be required to include more terms of the Taylor series in getting the mean and the variance.