Definition:Uniform Distribution/Continuous

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

$X$ is said to be uniformly distributed on the interval $\left[{a \,.\,.\, b}\right]$ if it has probability density function:


 * $\displaystyle f_X \left({x}\right) = \begin{cases} \frac 1 {b - a} & a \le x \le b \\ 0 & \text{otherwise} \end{cases}$

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

This is written:


 * $X \sim \operatorname U \left[{a \,.\,.\, b}\right]$

Also see

 * Discrete Uniform Distribution