21.4.7.1. Normal Distribution

One of most commonly used distribution in engineering is the normal distribution. The probability density function (PDF) of the distribution is expressed as

\({{f}_{X}}(x)=\frac{1}{{{\sigma }_{X}}\sqrt{2\pi }}\exp \left[ -\frac{1}{2}{{\left( \frac{x-{{\mu }_{X}}}{{{\sigma }_{X}}} \right)}^{2}} \right],-\propto \le x\le +\propto\)

where the mean (\({{\mu }_{X}}\)) and the standard deviation (\({{\sigma }_{X}}\)) are the two parameters of the distribution.