Problem 3: Suppose that X₁, X₂, ..., X, are i.i.d. random variables on the interval [0, 1] with the density function: f (x; a) = Г(3а) r(a)r(2a) where I' is the

gamma function and where a > 0 is a parameter to be estimated from the sample. Given that E(X) x-1(1-x)²α-1 Var (X) = = 2 9(3a + 1) a) Find the method of moments estimator of a. b) Write out the equation for the maximum likelihood estimator of a.