Mathematics · Statistical Inference
Suppose X1, X2, ..., Xn are independent and identically distributed (i.i.d.) random variables following a Uniform(θ, 2θ) distribution, where θ > 0. Let X(1) = min{X1, ..., Xn} and X(n) = max{X1, ..., Xn}. Which of the following statements is correct?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1(X(1), X(n)) is jointly sufficient and complete for θ
- 2(X(1), X(n)) is jointly sufficient but not complete for θ✓
- 3X(1) alone is a sufficient statistic for θ
- 4X(n) alone is a complete statistic for θ
Correct answer
(X(1), X(n)) is jointly sufficient but not complete for θ
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