Question: Let X1, X2, . . . , Xn be i.i.d. variables with p.d.f. as follows: f(x|) = x^1 , for 0 < x < 1,

Let X1, X2, . . . , Xn be i.i.d. variables with p.d.f. as follows:

f(x|) = x^1 , for 0 < x < 1,

0, otherwise.

Suppose that > 0 is an unknown parameter.

(1) Find the method-of-moments estimator, (1) n , for and show its consistency.

(2) Find the M.L.E., n^(2) , of and show that n ( (2) n )/. N(0, 1)

as n .

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