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Hej,

I am studying a proof for the Markov inequality, and there is a certain step, which I don't understand:

$\mathbb{E}(X \cdot \mathbb{I}_A) \ge \mathbb{E}(a \mu \mathbb{I_A})$

where $\mathbb{I}_A$ is the indicator function, $\mu = \mathbb{E}(X)$ and $A = [X \ge a \cdot \mathbb{E}(X)]$.

Thanks for any help.

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    What is $\Bbb X$?2012-12-03
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    I downvoted for the following reasons: 1. as $\Bbb X$ is not defined, the problem is unclear; 2. There is no attempt shown.2012-12-03
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    Sorry, that was a typing mistake. I just have in the proof the following inequalities: $\mu = \mathbb{E}(X) \ge \mathbb{E}(X \cdot \mathbb{I}_A) \ge \mathbb{E}(a \cdot \mu \cdot \mathbb{I}_A) = a \mu \mathbb{P}[X \ge a \cdot \mu]$, which proofs the Markov inequality. But the step above is unclear. Why is this inequality correct?2012-12-03

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