Definition:Uniform Distribution/Continuous

Definition
Let $X$ be a continuous random variable on a probability space $\struct {\Omega, \Sigma, \Pr}$.

$X$ is said to be uniformly distributed on the closed real interval $\closedint a b$ if it has probability density function:


 * $\map {f_X} x = \begin{cases} \dfrac 1 {b - a} & a \le x \le b \\ 0 & \text{otherwise} \end{cases}$

for $a, b \in \R$, $a \ne b$.

This is written:


 * $X \sim \ContinuousUniform a b$

Also see

 * Discrete Uniform Distribution