Let X 1 , ..., X n (n ≥ 2) be a random sample from a U(-θ, 2θ) distribution, where θ > 0 is an unknown parameter. Let X (1) = min{X 1 , ..., X n } and X (n) = max{X 1 , ..., X n }. Which of the following statements is true?

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Mathematics · Mathematical Statistics

Let X 1 , ..., X n (n ≥ 2) be a random sample from a U(-θ, 2θ) distribution, where θ > 0 is an unknown parameter. Let X (1) = min{X 1 , ..., X n } and X (n) = max{X 1 , ..., X n }. Which of the following statements is true?

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The maximum likelihood estimator of θ is max{-X (1) , X (n) /2}

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Answer 1

The method of moments estimator of θ is 2X̄/3

Answer 2

The method of moments estimator of θ is 2X̄

Answer 3

The maximum likelihood estimator of θ is max{-X (1) , X (n) /2}

Answer 4

The maximum likelihood estimator of θ is min{-X (1) , X (n) /2}

Let X 1 , ..., X n (n ≥ 2) be a random sample from a U(-θ, 2θ) distribution, where θ > 0 is an unknown parameter. Let X (1) = min{X 1 , ..., X n } and X (n) = max{X 1 , ..., X n }. Which of the following statements is true?

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Let X 1 , ..., X n (n &ge; 2) be a random sample from a U(-&theta;, 2&theta;) distribution, where &theta; > 0 is an unknown parameter. Let X (1) = min{X 1 , ..., X n } and X (n) = max{X 1 , ..., X n }. Which of the following statements is true?

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Let X 1 , ..., X n (n ≥ 2) be a random sample from a U(-θ, 2θ) distribution, where θ > 0 is an unknown parameter. Let X (1) = min{X 1 , ..., X n } and X (n) = max{X 1 , ..., X n }. Which of the following statements is true?