## 2.11.4 Gaussian PDFA random variable Y is said to have a Gaussian or normal pdf if The mean, variance, and s-transforms are The Gaussian pdf arises most often in practice in applications of the Central Limit Theorem, which states (roughly) that the pdf of
the sum of a large number of independent random variables approaches
a Gaussian pdf with mean equal to the sum of the individual means
and variance equal to the sum of the individual variances. The analyst
of urban service systems should be familiar with this application of
the Gaussian pdf. On occasion in this text we may invoke the Central
Limit Theorem to approximate the pdf of a sum of random variables as
a Gaussian random variable. Since we cannot obtain a closed-form
expression for a partial integral of f_{y}(y), tables of the Gaussian
pdf and cdf are widely available, for instance in mathematics and
engineering handbooks. |