Definition:Beta Distribution

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

Let $\Img X = \closedint 0 1$.

$X$ is said to have a Beta distribution if it has probability density function:


 * $\map {f_X} X = \dfrac {x^{\alpha - 1} \paren {1 - x}^{\beta - 1} } {\map \Beta {\alpha, \beta} }$

for $\alpha, \beta > 0$, where $\Beta$ is the Beta function.

This is written:


 * $X \sim \BetaDist \alpha \beta$