Wikipedia:Reference desk/Archives/Mathematics/2007 October 26

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October 26

3-sphere of convergence?--from talk page of radius of convergence

Suppose one had a power series w/radius of conv = 1, say, around z=0, say. If z were allowed to be quaternionic, then the boundary of convergence would be a 3 sphere of rad 1. I bet the subset of the boundary where the series converges could be quite beautiful and fascinating. Does anyone know of results/research in this area? It would be a great addition to put in this article.Rich 07:47, 25 September 2006 (UT --I've moved this here from article talk page. Thanks.--Rich Peterson130.86.14.25 03:17, 26 October 2007 (UTC)

three dice

what would a q-q plot of 3d6 dice look like? i'm wondering how normal the distribution is.--Sonjaaa 06:45, 26 October 2007 (UTC)

It a pretty good approximation. You can work out the expected frequencies fairly easily, there 216 different combinations of the three dice and the number times each score is achived can be worked out. From these the mean and standard deviation can be calculated (10.5 and 2.96) and then predicted normal frequencies. The following table shows the frequencies

score  3   4   5    6    7    8    9   10   11   12   13   14   15  16  17  18
3d6    1   3   6   10   15   21   25   27   27   25   21   15   10   6   3   1
normal 1.2 2.7 5.2  9.2 14.5 20.4 25.5 28.6 28.6 25.5 20.4 14.5  9.2 5.2 2.7 1.2

which are pretty close, you could calculate the Kurtosis and 3D6 is slightly leptokurtic. --Salix alba (talk) 23:45, 26 October 2007 (UTC)

I've made the claim, without anything other than an intuitive sense that it seemed right, that as n →∞, the distribution of nd6 approaches a normal curve. (and more generally, that this holds true, no matter the number of sides on the dice). Was I misleading my students when I made this claim? Donald Hosek 00:51, 27 October 2007 (UTC)

No, you was not misleading. The section Multiset#Cumulant generating function explains why. Bo Jacoby 06:56, 27 October 2007 (UTC).

The tendency to normality as n increases is also a consequence of the Central Limit Theorem, requiring only a finite variance in the distribution.→81.154.108.210 09:17, 27 October 2007 (UTC)

I got a kurtosis of -0.577, which is apparently called platykurtic. -- Meni Rosenfeld (talk) 10:30, 27 October 2007 (UTC)