The relationship between the Gaussian Curve and Pascal's Triangle Coefficients
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From: A N Niel on 10 Mar 2010 14:54 In article <b6d44537-cd88-4603-a2d8-3dd0d4dc7fe7(a)i25g2000yqm.googlegroups.com>, 2.7182818284590... <tangent1.57(a)gmail.com> wrote: > Very good!!! I had that feeling as well. Do you know where I can > find the proof of this Feller, as the other reply said. > (i.e. Gaussian Distribution is a Binomial > Distribution with infinity outcomes)? but this part is nonsense.
From: gudi on 10 Mar 2010 15:38
On Mar 10, 10:51 pm, "2.7182818284590..." <tangent1...(a)gmail.com> wrote: > On Mar 9, 8:55 pm, Frisbieinstein <patmpow...(a)gmail.com> wrote: > > > > > > > On Mar 10, 6:11 am, "2.7182818284590..." <tangent1...(a)gmail.com> > > wrote: > > > > What is the relationship between the Gaussian Curve and the > > > coefficients of Pascal's Triangle? When I plot the coefficients of PT > > > for the 15th row, it looks very much like a Gaussian Distribution. > > > > 1 16 > > > 16 15 > > > 120 14 > > > 560 13 > > > 1820 12 > > > 4368 11 > > > 8008 10 > > > 11440 9 > > > 12870 8 > > > 11440 7 > > > 8008 6 > > > 4368 5 > > > 1820 4 > > > 560 3 > > > 120 2 > > > 16 1 > > > 1 0 > > > > So how are these two phenomenon's related? Coincidentally, or is the > > > Binomial Distribution the basis for the Gaussian Distribution? > > > They are very similar. You can think of the Gaussian as the limit as > > the number of trials goes to infinity. > > Very good!!! I had that feeling as well. Do you know where I can > find the proof of this (i.e. Gaussian Distribution is a Binomial > Distribution with infinity outcomes)? Gaussian curve is the limit as the number of trials goes to infinity. It is also shown in above Ray Vickson referred Wikipaedia demo. Narasimham |