Continuous Uniform Distribution

A kind of Continuous Distribution where each Outcome has uniform (equal) Probability Density.

$$X\sim U(a,b)\text{where}a<x<b$$

• $f(x)=\frac{1}{b-a}$
• $E(X)=\frac{a+b}{2}$
• $\text{Var}(X)=\frac{(a-b{)}^2}{12}$
• $F_X(x)={\int }_a^{x}f(t)dt={\int }_a^x\frac{1}{b-a}=\frac{x-a}{b-a}$