: 推 zevin:你可视它为定义，定义pdf长那样的机率分配为常态分配 10/10 17:31 : → zevin:或者你应该问，为什麽要把pdf长那样的机率分配叫做常态分配 10/10 17:36 : 推 daa94:但是老师要我推导公式证明Orz....我已经弄一整天了 呜 10/10 17:43 : 推 zevin:但是你给的这个网页，下面也有写说这是常态分布的定义..... 10/10 17:53 : 推 zevin:我学了很久的统计跟机率，也没听过常态pdf的证明 10/10 17:57 : → zevin:一般而言都是视为定义吧 10/10 17:58 应该不是定义喔. 很多 distribution 都是依据一些性质而推导出来的, 不是可以爱定成怎样就怎样. 比如有名的 Poisson distribution 也是根据一些假设的性质而推导出来的. 给原 po, 我不知道到底怎麽导出来的. 但是我看了一下 wiki, 里面提到最初的文章是跟中央极限定理有关. (我猜大概是 Binomial 在 n 很大时收敛到的 distribution 称为 normal, 诸如此类的) 听说学长们以前上机率课印象中老师有推导过, 似乎是从 wiki 里提到从重复的 experiments然後看 errors, 设了一些假设然後可以推导出 normal 的 pdf. 不过真的不记得了. 你可以从这几个方向去查查看有没有帮助. Google 一下这些前辈的文章等等. 我顺便附上 wiki 的解释 History The normal distribution was first introduced by Abraham de Moivre in an article in 1734 (reprinted in the second edition of his The Doctrine of Chances, 1738) in the context of approximating certain binomial distributions for large n. His result was extended by Laplace in his book Analytical Theory of Probabilities (1812), and is now called the theorem of de Moivre-Laplace. Laplace used the normal distribution in the analysis of errors of experiments. The important method of least squares was introduced by Legendre in 1805. Gauss, who claimed to have used the method since 1794, justified it rigorously in 1809 by assuming a normal distribution of the errors. The name "bell curve" goes back to Jouffret who first used the term "bell surface" in 1872 for a bivariate normal with independent components. The name "normal distribution" was coined independently by Charles S. Peirce, Francis Galton and Wilhelm Lexis around 1875. This terminology is unfortunate, since it reflects and encourages the fallacy that many or all probability distributions are "normal". (See the discussion of "occurrence" below.) That the distribution is called the Gaussian distribution is an instance of Stigler's law of eponymy: "No scientific discovery is named after its original discoverer." --

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