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Thread: Finite conditional expectation

  1. July 5th 2010, 11:41 PM #1
    batman
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    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.
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  2. July 6th 2010, 05:12 AM #2
    Focus
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    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]
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