Consider a random sample X1, … , Xn from the pdf f (x; u) = .5(1 + (THETA)x) -1 <= x <= 1 where -1 <= theta <= 1 (this distribution arises in particle physics). Show that theta = 3X is an unbiased estimator of theta. [Hint: First determine mu = E(X) = E(X).]

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.