The Gamma distributionwith paramters

fa,f (x) =Fox -e Ox for allx 2 0. The I function is defined by T (s) = xtte * dx. As usual, the constant - is a normalization constant that gives ffa,, (x) dx = 1. In this problem, let X1, ..., Xn be i.i.d. Gamma variables with B = -for some a > 0. That is, X1, ..., Xn ~ Gamma (a, . random variables for some a > 0. The pdf for X; is therefore 1 fa (x) =T(a)ga x -e x/a, for all x 2 0.For the Delta method to apply, at what value ofx does g' need to be continuously differentiable? (Your answer should be in terms of a.) x: What distribution does r? converge to as n > oo? V" Gamma distribution 'A' Normal distribution "\" None of the above What is its asymptotic variance of 6;? Var (M) = Var (n)? 05)) = Using the previous part, find confidence intervals for a with asymptotic level 90% using both the "solving" and the "plug-in" methods. Use n = 25, and Xn = 4.5. (Enter your answers accurate to 2 decimal places. Use the Gaussian estimate go.05 ~ 1.6448 for best results.) Isolve = Iplug-in =