Answer is D 9. Suppose that X₁, X2,...,X₂ is a random sample from U(0, 0) distribution. It can be shown that the maximum likelihood estimator ofis 0 = max {X₁, X₂, ..., X} and furthermore, its sampling distribution is fax: 0) = {² for 0 < z ≤ 0, otherwise. Suppose we wish to use an estimator of the form ē= ce, such that is an unbiased estimator of 8. Then, what must the value of c be? (A) 1/(n+1) (B) 1/(n-1) (C) 1/n (D) (n+1)/n (E) n/(n+1)

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Answer is D
9. Suppose that X₁, X2,..., Xn is a random sample from U(0,0) distribution. It can be shown
that the maximum likelihood estimator of 0 is 0= max {X₁, X₂,..., X} and furthermore, its
sampling distribution is
f*(x: 0) =
- {*
0
(A) 1/(n +1)
(B) 1/(n-1)
(C) 1/n
(D) (n+1)/n
(E) n/(n+1)
for 0 < x≤ 0,
otherwise.
Suppose we wish to use an estimator of the form = ca, such that is an unbiased estimator
of 8. Then, what must the value of c be?
Transcribed Image Text:Answer is D 9. Suppose that X₁, X2,..., Xn is a random sample from U(0,0) distribution. It can be shown that the maximum likelihood estimator of 0 is 0= max {X₁, X₂,..., X} and furthermore, its sampling distribution is f*(x: 0) = - {* 0 (A) 1/(n +1) (B) 1/(n-1) (C) 1/n (D) (n+1)/n (E) n/(n+1) for 0 < x≤ 0, otherwise. Suppose we wish to use an estimator of the form = ca, such that is an unbiased estimator of 8. Then, what must the value of c be?
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