On 2/14/07, Henry Baker <hbaker1@pipeline.com> wrote:
Is there a simple/elegant/one-line proof that the coefficients of (1+x)^n approximate a Gaussian curve? I know that it is the convolution of n boxes, and that a large convolution of non-impulses approaches a Gaussian, but is there a quick/obvious proof of this that also gives you the appropriate mean & std deviation parameters?
I think that if you had an easy proof, people would get pretty excited. I know I would! All the intro stats texts I've ever seen talk about the central limit theorem (and even the fact that binomial coefficients approach a normal curve, which they also usually justify by the CLT) as being something beyond the scope of the course, requiring too much mathematical machinery and yielding not enough intuition. So if anyone sends you something, Henry, I'd love to see it! Or if you come up with something reasonably clean on your own. Thanks, --Joshua