Suppose X1,...,Xn are i.i.d. real-valued random variables. Write Xi = X+ i X i , where

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Suppose X1,...,Xn are i.i.d. real-valued random variables.

Write Xi = X+

i − X−

i , where X+

i = max(Xi, 0). Suppose X−

i has a finite mean, but X+

i does not. Let X¯n be the sample mean. Show X¯n P

→ ∞. Hint: For B > 0, let Yi = Xi if Xi ≤ B and Yi = B otherwise; apply the Weak Law to Y¯n.

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Testing Statistical Hypotheses

ISBN: 9781441931788

3rd Edition

Authors: Erich L. Lehmann, Joseph P. Romano

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Question Posted: Nov 02, 2024 05:01 AM

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Suppose X1,...,Xn are i.i.d. real-valued random variables. Write Xi = X+ i X i , where

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Testing Statistical Hypotheses

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