“central limit theorem”的概念、定义、翻译、参考文献-科学参考

central limit theorem

Statistics

A theorem, proposed by Laplace, explaining the importance of the normal distribution in Statistics. Let X₁, X₂,…, X_n be independent random variables each having the same distribution, with mean μ and variance σ². Let X̄, given by $central limit theorem$ denote the sample mean. The central limit theorem states that, for large n, the distribution of X̄ is approximately a normal distribution with mean μ and variance ${1 \\over n}$σ². Thus, for a large random sample of observations from a distribution with mean μ and variance σ², the distribution of the sample mean is approximately normal with mean μ and variance ${1 \\over n}$σ² and the distribution of the sample total is approximately normal with mean nμ and variance nσ². The phrase ‘central limit theorem’ appears in the title (in German) of an article by Pólya published in 1920.

Electronics and Electrical Engineering

A statistical theorem which states that, in general, the probability distribution of the sum of a number of statistically independent random variables approximates to the Gaussian distribution as the number of variables becomes very large, irrespective of the distributions of the individual random variables. The central limit theorem is commonly used in the understanding and analysis of noise in communication systems.

Geology and Earth Sciences

In statistics, the theorem stating of a series of data sets drawn from any probability distribution, that the distribution of the means of those data sets will follow a normal distribution.

单词	central limit theorem
释义	central limit theorem Statistics A theorem, proposed by Laplace, explaining the importance of the normal distribution in Statistics. Let X₁, X₂,…, X_n be independent random variables each having the same distribution, with mean μ and variance σ². Let X̄, given by $central limit theorem$ denote the sample mean. The central limit theorem states that, for large n, the distribution of X̄ is approximately a normal distribution with mean μ and variance ${1 \\over n}$σ². Thus, for a large random sample of observations from a distribution with mean μ and variance σ², the distribution of the sample mean is approximately normal with mean μ and variance ${1 \\over n}$σ² and the distribution of the sample total is approximately normal with mean nμ and variance nσ². The phrase ‘central limit theorem’ appears in the title (in German) of an article by Pólya published in 1920. Electronics and Electrical Engineering A statistical theorem which states that, in general, the probability distribution of the sum of a number of statistically independent random variables approximates to the Gaussian distribution as the number of variables becomes very large, irrespective of the distributions of the individual random variables. The central limit theorem is commonly used in the understanding and analysis of noise in communication systems. Geology and Earth Sciences In statistics, the theorem stating of a series of data sets drawn from any probability distribution, that the distribution of the means of those data sets will follow a normal distribution.
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