General Studies · Order Statistics
Let X1, X2, ..., Xn (n ≥ 3) be a random sample from the uniform distribution on the interval (θ1 - θ2, θ1 + θ2), where θ1 ∈ ℜ and θ2 > 0 are unknown parameters. Let X(r) be the rth order statistic, r = 1, 2, ..., n. Then, which of the following statements is true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1X(1) + X(n)2 is a complete statistic for θ1
- 2X(n) - X(1) is an unbiased estimator of θ2
- 3X(1) + X(n)2 is the uniformly minimum variance unbiased estimator (UMVUE) of θ1
- 4(n + 1)(X(n) - X(1))2(n - 1) is the uniformly minimum variance unbiased estimator (UMVUE) of θ2✓
Correct answer
(n + 1)(X(n) - X(1))2(n - 1) is the uniformly minimum variance unbiased estimator (UMVUE) of θ2
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