If X1,X2,...,Xn is a random sample from a distribution with pdf

Question

If X1,X2,...,Xn is a random sample from a distribution with pdf


f(x;θ)= 0<∞,0<θ<∞ , the pdf is equal to 0 elsewhere.



Show that Y=2(X-bar) is an unbiased estimator of θ and determine its efficiency.

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