Uniform Distribution

Def Uniform Distribution The probability density function of the continuous uniform distribution is: $f(x)=\{\begin{array}{ll}\frac{1}{b-a}& x\in [a,b]\\ 0& \text{otherwise}\end{array}$ And we write $X\sim \mathcal{U}(a,b)$ for random variable $X$.

Prop Uniform distribution is in the symmetric family.

Prop Expectation and Variance of Uniform Distribution $\mathbb{E}[X]=\frac{a+b}{2}\mathrm{Var}(X)=\frac{(b-a{)}^2}{12}$