The names Beta or β may refer to any of several distinct mathematical quantities.

For the Beta function, see Beta.

For the Beta distribution in statistics, see Statistics[Distributions][Beta].

For the non-central Beta distribution in statistics, see Statistics[Distributions][NonCentralBeta].

$\mathrm{convert}\left(\mathrm{{\rm B}}\left(x\,y\right)\,\mathrm{\Gamma }\right)$

$\frac{\mathrm{\Gamma }\left(x\right)\mathrm{\Gamma }\left(y\right)}{\mathrm{\Gamma }\left(y+x\right)}$

$\mathrm{with}\left(\mathrm{Statistics}\right)\:$

$X≔\mathrm{RandomVariable}\left(\mathrm{BetaDistribution}\left(a\,b\right)\right)$

$X≔\mathrm{\_R}$

$\mathrm{Variance}\left(X\right)$

$\frac{ab}{{\left(a+b\right)}^2\left(a+b+1\right)}$