Suppose that X1,X2,...,Xn are i.i.d random variables on the interval [0,1] with density function: F(x|alpha) = [gamme(2alpha)/[gamma(alpha)]^2] * [x(1-x)]^(alpha -1) where alpha > 0 is a parameter to be estimated from the sample. It can be shown that E[X] = 1/2 and Var[X] = 1/ [4(2alpha+1)] a. How does the shape of the density depend on alpha? b. How can the method of moments be used to estimate alpha?c. What equation does the m.l.e. of alpha satisfy? d. What is the asymptotic variance of the m.l.e.?