Let X1, X2, ..., X13 be independent and identically distributed (i.i.d.) Poisson(θ) random variables, where θ > 0. Then, which of the following statements is true?

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Mathematics · Mathematical Statistics

Let X1, X2, ..., X13 be independent and identically distributed (i.i.d.) Poisson(θ) random variables, where θ > 0. Then, which of the following statements is true?

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(∑i=17 Xi)(∑i=813 Xi) is an unbiased estimator of 42θ2.

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Answer 1

(∑i=17 Xi)(∑i=813 Xi) is an unbiased estimator of 42θ2.

Answer 2

16 ∑i=813 Xi is the unique method of moments estimator of θ.

Answer 3

There does not exist any unbiased estimator of e-7θ.

Answer 4

e-X7 (∑i=16 Xi) (∑i=813 Xi) is a sufficient statistic for θ.

Let X1, X2, ..., X13 be independent and identically distributed (i.i.d.) Poisson(θ) random variables, where θ > 0. Then, which of the following statements is true?

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Let X1, X2, ..., X13 be independent and identically distributed (i.i.d.) Poisson(θ) random variables, where θ > 0. Then, which of the following statements is true?

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