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 $\alpha, \beta \gt 0$. $B(\alpha, \beta)$ is the beta function.

Note that the pdf function is plotted as a function of $x$ and $\beta$ for a specified $\beta/\alpha$ ratio.