Template:Alta exponential mean

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}= & \mathop{}_{0}^{\infty }t\cdot f(t)dt=\mathop{}_{0}^{\infty }t\cdot \lambda \cdot {{e}^{-\lambda t}}dt \\ & = & \frac{1}{\lambda } \end{align} }[/math]