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(α,β)Beta(\alpha, \beta) is given by

f(x;α,β)=Γ(α+β)Γ(α)Γ(β)xα1(1x)β1.f(x; \alpha, \beta) = \frac{\Gamma(\alpha + \beta)}{\Gamma(\alpha)\Gamma(\beta)}x^{\alpha - 1}(1 - x)^{\beta - 1}.