Template:Normal probability density function

Normal Probability Density Function

The [math]\displaystyle{ pdf }[/math] of the normal distribution is given by:

[math]\displaystyle{ f(t)=\frac{1}{\sigma \sqrt{2\pi }}{{e}^{-\frac{1}{2}{{\left( \frac{t-\mu }{\sigma } \right)}^{2}}}} }[/math]

where:

[math]\displaystyle{ \mu }[/math] = mean of the normal times-to-faiure, also noted as \bar T

[math]\displaystyle{ \theta=\text{standard deviation of the times-to-failure} }[/math]

It is a two-parameter distribution with parameters [math]\displaystyle{ \mu }[/math] (or [math]\displaystyle{ \bar{T} }[/math] ) and [math]\displaystyle{ {{\sigma }} }[/math] , i.e. the mean and the standard deviation, respectively.