# Finite second moment

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• April 17th 2012, 10:39 PM
doug
Finite second moment
How to prove the followng statement: the second moment is finite (i.e. $\mathbb{E}(X^2) < \infty$) iff $\sum_{n=1}^{\infty} n \cdot \mathbb{P}(|X|>n)<\infty$.

I would really appreciate if you could help me!