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| ==Exponential Statistical Properties==
| | #REDIRECT [[Exponential Distribution Functions]] |
| ===The Mean or MTTF===
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| The mean, <math>\overline{T},</math> or mean time to failure (MTTF) is given by:
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| ::<math>\begin{align}
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| \bar{T}= & \int_{\gamma }^{\infty }t\cdot f(t)dt \\
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| = & \int_{\gamma }^{\infty }t\cdot \lambda \cdot {{e}^{-\lambda t}}dt \\
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| = & \gamma +\frac{1}{\lambda }=m
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| \end{align}</math>
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| Note that when <math>\gamma =0</math>, the MTTF is the inverse of the exponential distribution's constant failure rate. This is only true for the exponential distribution. Most other distributions do not have a constant failure rate. Consequently, the inverse relationship between failure rate and MTTF does not hold for these other distributions.
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| {{Median}}
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| {{Mode}}
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| {{Standard Deviation}}
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| {{Exponential Reliability Function}}
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| {{One-Parameter Exponential Reliability Function}}
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| {{Exponential Conditional Reliability}}
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| {{Exponential Reliable Life}}
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| {{Exponential Failure Rate Function}}
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