Statistics/Distributions/Uniform

The uniform distribution, as its name suggests, is a distribution with probability densities that are the same at each point in an interval. In casual terms, the uniform distribution shapes like a rectangle.

Mathematically speaking, the probability density function of the uniform distribution is defined as

$f\left(x\right)=\{\begin{array}{c}\frac{1}{b-a}\mathrm{\forall }realx\in [a,b]\end{array}$

And the cumulative distribution function is:

$F\left(x\right)=\{\begin{array}{cc}0,& \text{if }x\le a\\ \frac{x-a}{b-a},& \text{if }a<x<b\\ 1,& \text{if }x\ge b\end{array}$