Question: (20 points) Let X,..., Xn be a random sample from the p.d.f.: f(x; 0) = 0x2, x0>0 using factorization theorem. (a) Find sufficient statistic

(20 points) Let X,..., Xn be a random sample from the p.d.f.:

(20 points) Let X,..., Xn be a random sample from the p.d.f.: f(x; 0) = 0x2, x0>0 using factorization theorem. (a) Find sufficient statistic for (b) Find moment estimate 0 of 0 if it exists. (c) Find MLE of if it exists. (d) Is the MLE unbiased? Please justify. (e) Determine the Fisher information I(0). (f) Compute the variance of .

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