I want to prove the following but don't know how:
$\mathbb{E}X^2=\sum_{k=1}^\infty (2k-1)\mathbb{P}(X\ge k)$
I proved $\mathbb{E}X=\sum_{k=1}^\infty\mathbb{P}(X\ge k)$ before but I don't know if that helps here.
I want to prove the following but don't know how:
$\mathbb{E}X^2=\sum_{k=1}^\infty (2k-1)\mathbb{P}(X\ge k)$
I proved $\mathbb{E}X=\sum_{k=1}^\infty\mathbb{P}(X\ge k)$ before but I don't know if that helps here.
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