: 推 zevin:你可視它為定義，定義pdf長那樣的機率分配為常態分配 10/10 17:31 : → zevin:或者你應該問，為什麼要把pdf長那樣的機率分配叫做常態分配 10/10 17:36 : 推 daa94:但是老師要我推導公式證明Orz....我已經弄一整天了 嗚 10/10 17:43 : 推 zevin:但是你給的這個網頁，下面也有寫說這是常態分布的定義..... 10/10 17:53 : 推 zevin:我學了很久的統計跟機率，也沒聽過常態pdf的證明 10/10 17:57 : → zevin:一般而言都是視為定義吧 10/10 17:58 應該不是定義喔. 很多 distribution 都是依據一些性質而推導出來的, 不是可以愛定成怎樣就怎樣. 比如有名的 Poisson distribution 也是根據一些假設的性質而推導出來的. 給原 po, 我不知道到底怎麼導出來的. 但是我看了一下 wiki, 裡面提到最初的文章是跟中央極限定理有關. (我猜大概是 Binomial 在 n 很大時收斂到的 distribution 稱為 normal, 諸如此類的) 聽說學長們以前上機率課印象中老師有推導過, 似乎是從 wiki 裡提到從重複的 experiments然後看 errors, 設了一些假設然後可以推導出 normal 的 pdf. 不過真的不記得了. 你可以從這幾個方向去查查看有沒有幫助. Google 一下這些前輩的文章等等. 我順便附上 wiki 的解釋 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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