Mathematics · Statistical Inference
Suppose that X 1 , X 2 , ..., X n are independent and identically distributed Poisson (λ) random variables, where λ > 0 is unknown. Which of the following statements is true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1( n - 2 n ) ∑ i=1 n X i is an inconsistent estimator of e -2λ .
- 2( n - 2 n ) ∑ i=1 n X i is the minimum variance unbiased estimator (MVUE) of e -2λ .✓
- 31 n ∑ i=1 n (-1) X i is an inconsistent estimator for e -2λ .
- 41 n ∑ i=1 n (-1) X i is a biased estimator of e -2λ .
Correct answer
( n - 2 n ) ∑ i=1 n X i is the minimum variance unbiased estimator (MVUE) of e -2λ .
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