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 }_{T}}\sqrt{2\pi }}{{e}^{-\tfrac{1}{2}{{\left( \tfrac{T-\mu }{{{\sigma }_{T}}} \right)}^{2}}}} }[/math]

where:

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

[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 }_{T}} }[/math] , i.e. the mean and the standard deviation, respectively.