Template:Alta exponential mean: Difference between revisions

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::<math>\begin{align}
::<math>\begin{align}
\overline{T}& = \mathop{}_{0}^{\infty }t\cdot f(t)dt=\mathop{}_{0}^{\infty }t\cdot \lambda \cdot {{e}^{-\lambda t}}dt \\  
\overline{T}& = \int_{0}^{\infty }t\cdot f(t)dt=\int_{0}^{\infty }t\cdot \lambda \cdot {{e}^{-\lambda t}}dt \\  
& = \frac{1}{\lambda }   
& = \frac{1}{\lambda }   
\end{align}</math>
\end{align}</math>

Revision as of 23:26, 6 February 2012

The Mean or MTTF

The mean, [math]\displaystyle{ \overline{T}, }[/math] or Mean Time To Failure (MTTF) of the 1-parameter exponential distribution is given by:

[math]\displaystyle{ \begin{align} \overline{T}& = \int_{0}^{\infty }t\cdot f(t)dt=\int_{0}^{\infty }t\cdot \lambda \cdot {{e}^{-\lambda t}}dt \\ & = \frac{1}{\lambda } \end{align} }[/math]