Quoting Henry Baker <hbaker1@pipeline.com>:
Why should a discrete distribution (the binomial coefficients) approach the continuous distribution ~ exp(-(x/sigma)^2/2), ...
from taking limits, specifically, Stirling's approximation of factorials.
... and where does the sigma come from in the binomial distribution?
the epsilon in my original posting. The x^2 in the Gaussian comes from the pairing (ave + eps)(ave - eps). By the way, some careless editing on my part of the "reply" function has resulted in a doubling of these postings.
http://en.wikipedia.org/wiki/Normal_distribution
The proof given in this article still doesn't seem to me to be transparent enough:
Although Weisstein's pages, wikipedia, and similar are quite useful and informative, they are not always reliable, and often propagate common misconceptions and inaccurate folklore. Anyway, I was just trying to answer the original question about an interesting coincidence with a simple and plausible explanation. One can fancy up the details, but I sure wish somebody had used this explanation when I wes first studying statistics. I have used it in my own classes, somplete with a derivation of Stirling's formula, so I have confidence in its accuracy. Sorry I can't relate the epsilon to sigma; as I recall, it is essentially the standard deviation according to how much you keep missing the average, but there are some pi's and factors of 2 and the like, so as I recall there is some scaling involved. - hvm ------------------------------------------------- www.correo.unam.mx UNAMonos Comunicándonos