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1. Obtain the efficiency of the estimator. Is it a fully efficient estimator? Give reasons to...

1. Obtain the efficiency of the estimator. Is it a fully efficient estimator? Give reasons to support your conclusions.

Suppose that x1, . . . , xn are a random sample from f(x; θ) = (θ + 1)x^θ , 0 < x < 1

Here the parameter θ must satisfy that θ > −1.

We know I(θ) = n/(1 + θ)^2 and the MOM estimator based on the first moment is ˆθ = (1 − 2¯x)/(¯x − 1)

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