# Distribusyong Beta

Parameters Probability density function Cumulative distribution function ${\displaystyle \alpha >0}$ shape (real)${\displaystyle \beta >0}$ shape (real) ${\displaystyle x\in (0;1)\!}$ ${\displaystyle {\frac {x^{\alpha -1}(1-x)^{\beta -1}}{\mathrm {B} (\alpha ,\beta )}}\!}$ ${\displaystyle I_{x}(\alpha ,\beta )\!}$ ${\displaystyle {\frac {\alpha }{\alpha +\beta }}\!}$ ${\displaystyle I_{0.5}^{-1}(\alpha ,\beta )}$ no closed form ${\displaystyle {\frac {\alpha -1}{\alpha +\beta -2}}\!}$ for ${\displaystyle \alpha >1,\beta >1}$ ${\displaystyle {\frac {\alpha \beta }{(\alpha +\beta )^{2}(\alpha +\beta +1)}}\!}$ ${\displaystyle {\frac {2\,(\beta -\alpha ){\sqrt {\alpha +\beta +1}}}{(\alpha +\beta +2){\sqrt {\alpha \beta }}}}}$ see text see text ${\displaystyle 1+\sum _{k=1}^{\infty }\left(\prod _{r=0}^{k-1}{\frac {\alpha +r}{\alpha +\beta +r}}\right){\frac {t^{k}}{k!}}}$ ${\displaystyle {}_{1}F_{1}(\alpha ;\alpha +\beta ;i\,t)\!}$