In the Journal of Statistical Computation and Simulation (Vol. 67, 2000), researchers presented a numerical procedure for estimating the parameters of a beta distribution. The method involves a re-parameterization of the probability density function. Consider a beta distribution with parameters α* and β*, where α* = αβ and β* = β(1 - α).
a. Show that the mean of this beta distribution is α.
b. Show that the variance of this beta distribution is α(1 - α)/(β + 1).