Beta probability density function (pdf): \[f(x; \alpha, \beta) = \frac1{B(\alpha, \beta)}x^ { \alpha-1 }(1 - x) ^ { \beta -1 } \]
where $0 \le x \le 1$ and the shape parameters $\alpha, \beta \gt 0$. The beta function $B(\alpha, \beta)$ is a normalization constant to ensure the total probability integrates to 1.