Home page for accesible maths 2.2 Review of Continuous random variables 2.2.1 Uniform Distribution 2.3 Normal distribution

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2.2.2 Exponential Distribution

The Exponential distribution (not to be confused with the exponential function) is used to model distances between successive counts of a Poisson process, i.e. time between earthquakes, time between calls. The parameter of interest, $\theta$ is often referred to as the rate. Some properties of Exponential random variables include:

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Mean = $1/\theta$ .
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Variance = $1/\theta^{2}$ .
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PDF:

$f(x)=\left\{\begin{array}[]{ll}0,&x\leq 0\\ \theta\exp{(-\theta x)},&x\geq 0\end{array}\right.$
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CDF:

$F(x)=\left\{\begin{array}[]{ll}0,&x\leq 0\\ 1-\exp{(-\theta x)},&x\geq 0\end{array}\right.$