Several fundamental facts of mathematical statistics describe this phenomenon, including the law of large numbers and the central limit theorem.
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Basic probability theory : the law of large numbers, the central limit theorem ( derivation from the Fourier transform ).
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It reflects, in particular, on the properties described by the law of large numbers and the central limit theorem.
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Marquis de Laplace proved the central limit theorem in 1810, consolidating the importance of the normal distribution in statistics . ]]
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However convergence in distribution is very frequently used in practice; most often it arises from application of the central limit theorem.
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The classical central limit theorem describes the size and the distributional form of the stochastic fluctuations around the deterministic number during this convergence.
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With relatively large samples, however, a central limit theorem can be invoked such that hypothesis testing may proceed using asymptotic approximations.
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Lindeberg's work wasn't known by Alan Turing, who proved the central limit theorem in his disseration in 1935.
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Alternatively, this result can also be demonstrated by applying a multidimensional generalization of the central limit theorem, or through symmetry arguments.
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See also our articles Binomial distribution and Central limit theorem .-- Talk 15 : 50, 12 April 2007 ( UTC)
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