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Given $X$ follows some distribution with cdf $\Phi$, how can I find $E[X\Phi(X)]$? (The question is for normal so integrating is a bit difficult). I also realize that $\Phi(X)$ follows Uniform distribution

Numerical methods suggest the answer is about $0.28$

Any hints?


marked as duplicate by Anvit, Community Apr 7 at 17:02

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