Exponential Distribution

probability-theory

Definition

Exponential Distribution

The exponential distribution models waiting times (continuous analogue to the Geometric distribution) with density $f$ given as:

$$f(x)=\{\begin{array}{ll}\lambda e^{-\lambda x}& \text{for}x\ge 0\\ 0& \text{else}\end{array}$$

for $\lambda \in (0,\infty )$.

Expected Value

The expectation is given by:

$$\mathbb{E}[X]=\frac{1}{\lambda }$$

Variance

The variance is given by:

$$\mathbb{V}ar(X)=\frac{1}{{\lambda }^2}$$