Beta Type I Distribution
A continuous random variable $X$ is said to have a beta type I distribution with parameter $\alpha$ and $\beta$ if its p.d.f. is given by
$$ \begin{aligned} f(x)&=\frac{1}{B(\alpha,\beta)}x^{\alpha-1}(1-x)^{\beta-1}, 0<x<1; \alpha, \beta > 0. \end{aligned} $$
Mean of Beta Type I Distribution
The mean of beta type I distribution is
$E(X) = \dfrac{\alpha}{\alpha+\beta}$.
Variance of Beta Type I Distribution
The variance of beta type I distribution is
