# 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 and only 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 $\Beta$ denotes the Beta function.

This is written:

$X \sim \BetaDist \alpha \beta$

## Also see

• Results about the Beta distribution can be found here.

## Technical Note

The $\LaTeX$ code for $\BetaDist {\alpha} {\beta}$ is \BetaDist {\alpha} {\beta} .

When the arguments are single characters, it is usual to omit the braces:

\BetaDist \alpha \beta