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A random sample X1, X2, . . . , Xn is drawn from a population with...

A random sample X1, X2, . . . , Xn is drawn from a population with pdf. f(x; β) = (3x^2)/(β^3) , 0 ≤ x ≤ β 0, otherwise

(a) [6] Find the pdf of Yn, the nth order statistic of the sample.

(b) [4] Find E[Yn].

(c) [4] Find Var[Yn].

(d)[3] Find the mean squared error of Yn when Yn is used as a point estimator for β

(e) [2] Find an unbiased estimator for β.

Math   Statistics-And-Probability   
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