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How does one compute [itex]\mathbb{E}\left(Xe^X\right)[/itex] and/or what is the outcome value?

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- Thread starter TaPaKaH
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How does one compute [itex]\mathbb{E}\left(Xe^X\right)[/itex] and/or what is the outcome value?

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$$\mathbb{E}[ X e^X ] = \int_{-\infty}^{\infty} x e^{x} e^{-(x - \mu)^2 / \sigma^2} \, dx$$

That's a tricky one, I don't think any of the common integration strategies really work.

WolframAlpha does give me an exact result for the standard distribution ##(\mu, \sigma) = (0, 1)##.

Maybe this will also help.

Sorry for the incomplete answer, hoping that this will get you started.

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Very nice one, and congratulations on post number 13,000!

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