Mathematics · Statistical Inference
Suppose X1, ..., Xn are i.i.d. N(θ, 1) random variables where θ ≥ 0. Let T be the maximum likelihood estimator (MLE) of θ. Which of the following statements is true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1Eθ(T) - θ ≥ 0 for all θ ≥ 0
- 2Eθ(T) - θ = 0 for all θ ≥ 0
- 3Eθ(T) - θ < 0 for all θ ≥ 0
- 4There exists θ0 > 0 such that Eθ(T) - θ 0 for all θ > θ0✓
Correct answer
There exists θ0 > 0 such that Eθ(T) - θ 0 for all θ > θ0
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