Question: X1, . .., Xn is an i.i.d. sample from Gamma distribution with the p.d.f of Xi: Ta) Bax-le x/B, x>0, f(x; a, B) = 0

X1, . .., Xn is an i.i.d. sample from Gamma distribution

X1, . .., Xn is an i.i.d. sample from Gamma distribution with the p.d.f of Xi: Ta) Bax-le x/B, x>0, f(x; a, B) = 0 otherwise. Let 3 = 0 > 0 be unknown parameter and a = 4. (a) (1 point) Find MLE 0 of 0; (b) (1 point) Check if 0 is unbiased; (c)* (1 point) Check if 0 is consistent (Hint: recall the sufficient conditions for consistency that involve Var(0), discussed on Nov. 17th lecture.) (d) (1 point) What is the asymptotic distribution of Vn(0 - 0)? (Hint: apply the CLT.)

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