7.31. Let Xg, X2,. . . , X denote a random sample of size n from a distribution with p.d.f. ..... 0 <x < 1, zero elsewhere, and 0 > 0.
(a) Show that the geometric mean (X1 X2... Xn)^1/n of the sample is a complete sufficient statistic for 0.
(b) Find the maximum likelihood estimator of 0, and observe that it is a function of this geometric mean.
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Geometric Mean, Maximum Likelihood Estimator (MLE) and Fisher-Neyman Factorization Theorem are investigated.