Beta Distribution

Notation:

$X \sim Beta(\alpha, \beta)$

Probability Density Function:

$f(x)=\frac{\Gamma(\alpha+\beta)}{\Gamma(\alpha)\Gamma(\beta)} x^{\alpha-1} (1-x)^{\beta-1}$

where:

Mean:

$\mathrm{E}[X]=\mu=\frac{\alpha}{\alpha+\beta}$

Variance:

$\mathrm{Var}[X]=\sigma^2=\frac{\alpha\beta}{(\alpha+\beta)^2(\alpha+\beta+1)}$

References:

  1. Beta Distribution - Wikipedia
  2. Beta Distribution - Wolfram MathWorld