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  2. Central limit theorem - Wikipedia

    en.wikipedia.org/wiki/Central_limit_theorem

    A curious footnote to the history of the Central Limit Theorem is that a proof of a result similar to the 1922 Lindeberg CLT was the subject of Alan Turing's 1934 Fellowship Dissertation for King's College at the University of Cambridge. Only after submitting the work did Turing learn it had already been proved.

  3. Lindeberg's condition - Wikipedia

    en.wikipedia.org/wiki/Lindeberg's_condition

    This theorem can be used to disprove the central limit theorem holds for by using proof by contradiction. This procedure involves proving that Lindeberg's condition fails for X k {\displaystyle X_{k}} .

  4. Lévy's continuity theorem - Wikipedia

    en.wikipedia.org/wiki/Lévy's_continuity_theorem

    Download as PDF; Printable version ... This theorem is the basis for one approach to prove the central limit theorem and is one of ... Rigorous proofs of this theorem ...

  5. Category:Theorems in statistics - Wikipedia

    en.wikipedia.org/wiki/Category:Theorems_in...

    Print/export Download as PDF; Printable version; In other projects ... Central limit theorem; Characterization of probability distributions;

  6. Method of moments (probability theory) - Wikipedia

    en.wikipedia.org/wiki/Method_of_moments...

    The method of moments was introduced by Pafnuty Chebyshev for proving the central limit theorem; Chebyshev cited earlier contributions by Irénée-Jules Bienaymé. [2] More recently, it has been applied by Eugene Wigner to prove Wigner's semicircle law, and has since found numerous applications in the theory of random matrices. [3]

  7. Normal distribution - Wikipedia

    en.wikipedia.org/wiki/Normal_distribution

    Comparison of probability density functions, () for the sum of fair 6-sided dice to show their convergence to a normal distribution with increasing , in accordance to the central limit theorem. In the bottom-right graph, smoothed profiles of the previous graphs are rescaled, superimposed and compared with a normal distribution (black curve).

  8. Illustration of the central limit theorem - Wikipedia

    en.wikipedia.org/wiki/Illustration_of_the...

    This section illustrates the central limit theorem via an example for which the computation can be done quickly by hand on paper, unlike the more computing-intensive example of the previous section. Sum of all permutations of length 1 selected from the set of integers 1, 2, 3

  9. Category:Central limit theorem - Wikipedia

    en.wikipedia.org/wiki/Category:Central_limit_theorem

    This page was last edited on 1 December 2024, at 08:30 (UTC).; Text is available under the Creative Commons Attribution-ShareAlike 4.0 License; additional terms may apply.

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