X1, ..., Xn is an i.i.d. sample from Gamma distribution with the p.d.f of Xi: 1 -1e B rilagaza-le=1/8, x > 0, xa Γ() f(x

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X1, ..., Xn is an i.i.d. sample from Gamma distribution with the p.d.f of Xi: 1 -1e B rilagaza-le=1/8, x > 0, xa Γ() f(x; a, 8) = 0 otherwise. Let B = 0 > O be unknown parameter and a = 4. (a) (1 point) Find MLE Ô of 0; (b) (1 point) Check if Ôn is unbiased; (c)* (1 point) Check if Ôn is consistent (Hint: recall the sufficient conditions for consistency that involve Var(ë), discussed on Nov. 17th lecture.) (d) (1 point) What is the asymptotic distribution of Vncên – 6)? (Hint: apply the CLT.) 7