Question: Let X 1 , . . . , Xn be a random sample from a distribution, whose pdf is fX ( x ; ) =

Let X1, . . . , Xn be a random sample from a distribution, whose pdf is

fX(x; ) = (1 1 )x 1, for x {1, 2, 3, . . . }.

Note that E(X) = 1/ and Var(X) = (1 1 )/2.

(a) Find the MM (method of moment) estimator for .

(b) Find the MLE (maximum likelihood estimator) for .

(c) Find a sufficient statistic for using the Factorization Theorem.

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