# Thread: Finite conditional expectation

1. ## Finite conditional expectation

I want the conditional expectation E[X|X>c] to be finite. I know X>=0. Is E[X]<infinity sufficient or do I need additional conditions? I'd think I need more (bounded second monent?), but I can't come up with an example for which E[X] is finite and E[X|X>c] is infinite.

2. Use the tower law and Jensen (conditional version).

Jensen: $|\mathbb{E}[X| \mathcal{F}] |\leq\mathbb{E}[|X| \, |\mathcal{F}]$

Tower law: $\mathbb{E}[\mathbb{E}[X| \mathcal{F}]]=\mathbb{E}[X]$