Continuous Uniform Distribution

Topics: Probability

Definition

The Continuous Uniform Distribution is a symmetric continuous probability distribution that describes an experiment with an arbitrary outcome that lies within certain bounds. The bound is defined by the minimum $a$ and the maximum $b$. $a$ and $b$ can be included in the interval $[a,b]$ or excluded from the interval $(a,b)$. All the values inside the interval are equally probable.

Probability Density Function

$$f(x) = \begin{cases} \frac{1}{b-a} \quad & a \leq x \leq b \\ 0 & x <a \;\; \& \;\; x>b \end{cases}$$

Cumulative Distribution function

$$F(x) = \begin{cases} 0 \quad \quad \quad & x<a \\ \frac{x-a}{b-a} & a \leq x \leq b \\ 1 & x > b \end{cases}$$

References

1. https://en.wikipedia.org/wiki/Continuous_uniform_distribution