Template:Normal probability density function: Difference between revisions
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The <math>pdf</math> of the normal distribution is given by: | The <math>pdf</math> of the normal distribution is given by: | ||
::<math>f(t)=\frac{1} | ::<math>f(t)=\frac{1}{\sigma \sqrt{2\pi }}{{e}^{-\frac{1}{2}{{\left( \frac{t-\mu }{\sigma } \right)}^{2}}}}</math> | ||
where: | |||
<math>\mu= \text{mean of the normal times-to-faiure, also noted as} \bar T </math> | <math>\mu= \text{mean of the normal times-to-faiure, also noted as} \bar T </math> | ||
Revision as of 17:55, 10 February 2012
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= \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 }} }[/math] , i.e. the mean and the standard deviation, respectively.