Mathematics · Mathematical Statistics

Let {X i : 1 ≤ i ≤ 2n} be independently and identically distributed normal random variables with mean μ and variance 1, and independent of a standard Cauchy random variable W. Which of the following statistics is consistent for μ?

Verified Solution4 OptionsUpdated: October 2026👁️1 View

Correct answer

n −1 (∑ i=1 n X i + W)

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Let {X i : 1 &le; i &le; 2n} be independently and identically distributed normal random variables with mean &mu; and variance 1, and independent of a standard Cauchy random variable W. Which of the following statistics is consistent for &mu;?