3. Let 3Lgt;0 and let XI.X2,...,X,, bearandomsample fromtltedistribution with probability density function 2 [(131) = 3.? e'l, xgt;0. zero

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3. Let 3L>0 and let XI.X2,...,X,, bearandomsample fromtltedistribution with probability density function2[(131) = 3.? e’lfi, x>0. zero otherwise.6 34Recall: |.t = 50:) = 3.? 02 = Var(x) = F.I . . .W= R has Gammn(a=2. 9= x) dismbutmn.. . - 6 . . 2n'l'heMoMemmatorofl Is 1 = ’fi; theMLEofl ts 3. = n—' n) Show that the MoM estimator i is asymptotically normally distributed (as n —> co).Find the parameters. 0) Show that the MLE i is asymptotically normally distributed (as n —> no ).Find the parameters. p) Findasufficientstatistic Y=u(Xl.X2. .Xn) for it.