Beta Distribution

For $\alpha >0,\beta >0$ on $x\in [0,1]$:

$$f(x)=\frac{x^{\alpha -1}(1-x{)}^{\beta -1}}{B(\alpha ,\beta )}$$

Expected Value

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

Variance

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