Question: Let X1, X2, ..., Xn be a random sample having the common pdf f(x, ) = 2 exp{2(x )} for x . (i) Show that

Let X1, X2, ..., Xn be a random sample having the common pdf

f(x, ) = 2 exp{2(x )} for x .

(i) Show that b = min(X1, X2, ..., Xn) is the MLE of .

(ii) Show that the pdf of b is f(x, ) = 2n exp{2n(x )} for x . (Hint: Find the common distribution function of Xi and use 1.1-6.)

(iii) Is b an unbiased estimator of ? Justify your answer

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