(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Prove that

E(X) > a.P(X>a)

2. Relevant equations

E(X) is expectation, a is a positive constant and X is the random variable.

(Note, > should be 'greater than or equal to' but I'm not too sure how to do it)

3. The attempt at a solution

Well I can show it easy enough for X~Exp(h), but of course this is not a general proof.

And I played around a bit with P(X>a)=1-F(a) where F is the cdf, but yeah. That's all I could really do. I just don't really get how the a factor comes in.

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# Homework Help: Expectation prob. Proof

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