Question: 2. Suppose you have an i.i.d. sample (X1, X2, ...... , X,) of size n from the pdf: f (x, 0 ) = =0 78,

2. Suppose you have an i.i.d. sample (X1, X2, ...... , X,) of size n from the pdf: f (x, 0 ) = =0 78, x20,0 >0. (a) Derive the moment generating function and find the mean E(X ) and the variance (b) Explain the basic idea in the method of moments (MM ) estimation and find the MM estimator 0, mm - (c) Explain the basic idea in maximum lieklihood (ML) estimation, and find the ML estimator Omi- (d) Are the MM and ML estimators of 0 unbiased and consistent estimators of 0? (e) Let another estimator On = Xn. Is 0, unbiased, efficient and consistent estimator of e

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