“Central Limit Theorem”的概念、定义、翻译、参考文献-科学参考

Central Limit Theorem

Mathematics

单词	Central Limit Theorem
释义	Central Limit Theorem Mathematics A fundamental theorem of statistics connects the distribution of a growing sample from a given distribution with the normal distribution. Formally, let X₁, X₂, X₃,…be a sequence of independent, identically distributed random variables with mean μ‎ and finite variance σ‎², and let ${\overset{―}{X}}_{n} = \frac{X_{1} + X_{2} + \dots + X_{n}}{n}, Z_{n} = \frac{({\overset{―}{X}}_{n} - μ)}{σ / \sqrt{n}} .$ Then, as n increases, the distribution of Z_n converges in distribution to the standard normal distribution with mean 0 and variance 1. It implies that for a large sample the sample mean has approximately the normal distribution with mean μ‎ and variance σ‎²/n. http://onlinestatbook.com/stat_sim/sampling_dist/index.html An applet that lets you define the population and then take multiple samples of different sizes to explore the behaviour of the Central Limit Theorem.
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