Template:Normal probability density function: Difference between revisions
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(Created page with '==Normal Probability Density Function== The <math>pdf</math> of the normal distribution is given by: ::<math>f(T)=\frac{1}{{{\sigma }_{T}}\sqrt{2\pi }}{{e}^{-\tfrac{1}{2}{{\…') |
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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( | ::<math>f(t)=\frac{1}{{{\sigma }_{t}}\sqrt{2\pi }}{{e}^{-\tfrac{1}{2}{{\left( \tfrac{t-\mu }{{{\sigma }} \right)}^{2}}}}</math> | ||
:where: | :where: | ||
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It is a two-parameter distribution with parameters <math>\mu </math> (or <math>\bar{T}</math> ) and <math>{{\sigma | It is a two-parameter distribution with parameters <math>\mu </math> (or <math>\bar{T}</math> ) and <math>{{\sigma }}</math> , i.e. the mean and the standard deviation, respectively. | ||
Revision as of 17:52, 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 }_{t}}\sqrt{2\pi }}{{e}^{-\tfrac{1}{2}{{\left( \tfrac{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.