Mathematics · Mathematical Statistics
Let X1, X2, ..., Xn be a random sample from an exponential distribution with probability density function f(x|θ) = e-(x-θ) if x ≥ θ, and 0 otherwise, where θ ∈ ℝ is an unknown parameter. If X(1) = min{X1, X2, ..., Xn}, then which of the following statements is true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1(X(1) - 1n ln 20, X(1)) is a 96% confidence interval for θ
- 2(X(1) - 1n ln 20, X(1)) is a 95% confidence interval for θ✓
- 3(X(1) - 2n ln 5, X(1)) is a 96% confidence interval for θ
- 4(X(1) - 2n ln 5, X(1)) is a 97% confidence interval for θ
Correct answer
(X(1) - 1n ln 20, X(1)) is a 95% confidence interval for θ
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