棣莫佛－拉普拉斯（de Movire - Laplace）定理，即服從二項分布的隨機變數序列的中心極限定理。它指出，參數為n, p的二項分布以np為均值、np(1-p)為方差的正態分布為極限。；本人學術水平有限只能從網上搜集樓主所需要的情報並且把它整理起來，以上都是大師們的手筆 我只是一個搬運工
在 Fourier transform and its application 一書裡面提到過一些，不知對你的問題有沒有幫助。
Several times we』ve met the idea that convolution is a smoothing operation. Let me begin with somegraphical examples of this, convolving a discontinuous or rough function repeatedly with itself. For homework you computed, by hand, the convolution of the rectangle function Π with itself a few times. Here are plots of this, up to Π ? Π ? Π ? Π.
Not only are the convolutions becoming smoother, but the unmistakable shape of a Gaussian is emerging.Is this a coincidence, based on the particularly simple nature of the function Π, or is something more going on? Here is a plot of, literally, a random function f(x) — the values f(x) are just randomly chosen numbers between 0 and 1 — and its self-convolution up to the four-fold convolution f ? f ? f ? f.
From seeming chaos, again we see a Gaussian emerging. The object of this section is to explain this phenomenon, to give substance to the following famous quotation: Everyone believes in the normal approximation, the experimenters because they think it is a mathematical theorem, the mathematicians because they think it is an experimental fact. G. Lippman, French Physicist, 1845–1921 The 「normal approximation」 (or normal distribution) is the Gaussian. The 「mathematical theorem」 here is the Central Limit Theorem. To understand the theorem and to appreciate the 「experimental fact」, we have to develop some ideas from probability.
