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Let $X \sim \Gamma(n , 1)$, I want to calculate $\mathbb{E}(|X - n|)$. Is there any good approach?

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Yes: compute the expectation of $X-n$ on the event $[X-n\geqslant0]$. –  Did Jan 27 '12 at 11:37
    
Any progress with the hint above? –  Did Mar 1 '12 at 8:05
    
@DidierPiau Currently no, I found it a bit hard to get the result. –  Fan Zhang Mar 4 '12 at 12:49
    
Do you know the density of the distribution of $X$? –  Did Mar 4 '12 at 15:50
    
Got something from the comments above? –  Did Aug 15 '12 at 15:50

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