# entropy of normal distribution [closed]

What is the entropy of a normal distribution with mean 0 and variance \sigma? Thanks!

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## closed as too localized by Andrey Rekalo, Yemon Choi, Qiaochu Yuan, Robin Chapman, Harald Hanche-OlsenJul 9 '10 at 23:39

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Typing the question into Google seems to give plenty of leads; also, Wikipedia looks to have answers that seem a bout right. Voting to close. –  Yemon Choi Jul 9 '10 at 20:42
Fine work on the World Cup. www1.voanews.com/english/news/sports/… –  Will Jagy Jul 9 '10 at 21:02

I found here that "the negative differential entropy of the normal distribution" (which may not be what you are asking for?) is: $$-\frac{1}{2} [ \log (2 \pi \sigma^2 ) + 1 ] ,$$ independent of $\mu$.
Octopus: Wikipedia is a big site. Care to tell us exactly what page you are looking at with a link? At en.wikipedia.org/wiki/Normal_distribution the table on the right at the top lists the entropy as $(1/2)\log(2\pi{e}\sigma^2)$, which is the same thing as $(1/2)log(2\pi\sigma^2) + 1/2$ since $\log(e) = 1$. So this is the same formula Joseph gives up to an overall minus sign (I wouldn't use "negative" entropy; the standard entropy formula should have an overall minus sign in it which cancels out that negative sign.) –  KConrad Jul 9 '10 at 21:12
@KConrad: Thanks for responding while I was out of touch! Yes, I think the discrepancy can be resolved by manipulations of $\log(e)$ and minus signs. –  Joseph O'Rourke Jul 9 '10 at 23:38