Uniform distribution

Definition:

• Continuous random variable
• $X\sim U(\alpha ,\beta )$
• $X$ is a uniform random variable on the interval $(\alpha ,\beta )$ if its Probability density function is given by:
  • $f(x)=\{\begin{array}{ll}\frac{1}{\beta -\alpha }& \text{if }\alpha <x\le \beta \\ 0& \text{otherwise}\end{array}$

Expected value $=\frac{\alpha +\beta }{2}$

Variance $=\frac{(b-a{)}^2}{12}$