Uniform Distribution

Notation:

$X \sim \mathcal{U}(a, b)$

Probability Density Function:

$$ f(x)= \begin{cases} \frac{1}{b-a} & \text{for x} \in [a, b] \\ 0 & \text{otherwise} \end{cases} $$

where:

Mean:

$\mathrm{E}[X]=\mu=\frac{1}{2}(a+b)$

Variance:

$\mathrm{Var}[X]=\sigma^2=\frac{1}{12}(b-a)^2$

References:

  1. Continuous Uniform Distribution - Wikipedia
  2. Uniform Distribution - Wolfram MathWorld