Uniform Continuous Probability Distribution

Definition

Uniform RV $X$ takes values in interval $[l,u],l<u\in \mathbb{R}$ s.t probability of any subinterval is proportional to its length: $P(a<X<b)=\frac{b-a}{u-l},\forall l\le a\le b\le u$

PDF Requirement

$$\{\begin{array}{ll}\frac{1}{u-l}& 1\le x\le u\\ 0& \text{otherwise}\end{array}$$

CDF Requirement

$$\{\begin{array}{ll}& \\ 0& x<1\\ \frac{x-l}{u-l}& 1\le x\le u\\ 1& x>u\end{array}$$