April 2014
Beginner to intermediate
830 pages
15h 21m
Chinese
Content preview from Mathematica 錦囊妙計
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12.4 示範中央極限定理（Central Limit Theorem）
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12.4 示範中央極限定理（Central Limit Theorem）
問題點
你想驗證中央極限定理（Central Limit Theorem，CLT），或對學生展示該定理。
解決方案
中央極限定理指出，對任意統計分布而言，當樣本數量足夠大時，樣本平均數的統計分
布將趨近於常態分布。為了展示中央極限定理，你可以由非常態分布中取數量夠多的亂
數，並將其平均。以下使用均勻分布（uniform distribution）作為範例。[Page-465]
討論說明
中 央 極 限 定 理 通 常 以 較 專 門 的 語 言 描 述， 在《
Statistics in a Nutshell
》 書 中， 作 者
Boslaugh 及 Watters 用簡單幾句話介紹：「中央極限定理所陳述的是，樣本平均數的抽
樣分布將近似於常態分 布，只 要數量夠大，對任何樣本統計分布均成 立（CLT states
that the sampling distribution of the sample mean approximates the normal distribution,
regardless of the distribution of the population from which samples are drawn, if the sample
size is sufficiently
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