Explorations

Nothing to see here. Give it a week or two...

But in the meanwhile, please enjoy this probability density function of a random Beta distribution (with an 80% credible interval marked):

Beta(3.00, 1.00) with 80% Credible Interval

The PDF of $Beta(\alpha, \beta)$ is given by

$f(x; \alpha, \beta) = \frac{\Gamma(\alpha + \beta)}{\Gamma(\alpha)\Gamma(\beta)}x^{\alpha - 1}(1 - x)^{\beta - 1}.$