How to prove the followng statement: the second moment is finite (i.e. $\displaystyle \mathbb{E}(X^2) < \infty $) iff $\displaystyle \sum_{n=1}^{\infty} n \cdot \mathbb{P}(|X|>n)<\infty$.
I would really appreciate if you could help me!
How to prove the followng statement: the second moment is finite (i.e. $\displaystyle \mathbb{E}(X^2) < \infty $) iff $\displaystyle \sum_{n=1}^{\infty} n \cdot \mathbb{P}(|X|>n)<\infty$.
I would really appreciate if you could help me!