中心极限定律

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--- 中心极限定律 [2024/03/15 04:53] – 2104龚文滕
+++ 中心极限定律 [2024/03/15 04:57] (当前版本) – 2104龚文滕
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-**标准误（standard of error）**，指样本均值分布的标准差，是反映样本均值分布变异性的指标。
+**标准误（standard of error）**
+  *指样本均值分布的标准差，是反映样本均值分布变异性的指标。
   *定义式为σ/√n，σ为总体的标准差，n为样本容量。
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   *The definition formula is σ/√n, σ is the standard deviation of the population, and n is the sample size.
+**大数定律（law of large numbers）**
-**大数定律（law of large numbers）**：随样本容量的的增大，样本均值与总体均值之间的误差会减小。
+  *随样本容量的的增大，样本均值与总体均值之间的误差会减小。
+  *Law of large numbers: As the sample size increases, the error between the sample mean and the population mean will decrease.
-  *Law of large numbers: As the sample size increases, the error between the sample mean and the population mean will decrease.
 **中心极限定律（central limit theorem）**
   *对于任何均值为μ，标准差为σ的总体, 样本容量为n的样本均值的分布，随着n趋近无穷大时，会趋近均值为μ，标准差为σ/√n的正态分布 。
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   *中心极限定律综合了样本均值的三个主要特性：形状、均值和方差。
-  *For any population with a mean of u and a standard deviation of u, and a sample size of n, the distribution of the mean will approach a normal distribution with a mean of u and a standard deviation of u/√ n as n approaches infinity.
+  *For any population with a mean of μ and a standard deviation of σ, and a sample size of n, the distribution of the mean will approach a normal distribution with a mean of μ and a standard deviation of σ/√n as n approaches infinity.
+  *Application conditions: Usually, when n ≥ 30, we believe that the distribution of sample mean satisfies the central limit theorem.
+  *The central limit theorem combines the three main characteristics of sample mean: shape, mean, and variance.

中心极限定律.1710478424.txt.gz · 最后更改: 2024/03/15 04:53 由 2104龚文滕