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• Central_limit_theorem abstract "In probability theory, the central limit theorem (CLT) states that, given certain conditions, the arithmetic mean of a sufficiently large number of iterates of independent random variables, each with a well-defined expected value and well-defined variance, will be approximately normally distributed, regardless of the underlying distribution. That is, suppose that a sample is obtained containing a large number of observations, each observation being randomly generated in a way that does not depend on the values of the other observations, and that the arithmetic average of the observed values is computed. If this procedure is performed many times, the central limit theorem says that the computed values of the average will be distributed according to the normal distribution (commonly known as a "bell curve").The central limit theorem has a number of variants. In its common form, the random variables must be identically distributed. In variants, convergence of the mean to the normal distribution also occurs for non-identical distributions or for non-independent observations, given that they comply with certain conditions.In more general probability theory, a central limit theorem is any of a set of weak-convergence theorems. They all express the fact that a sum of many independent and identically distributed (i.i.d.) random variables, or alternatively, random variables with specific types of dependence, will tend to be distributed according to one of a small set of attractor distributions. When the variance of the i.i.d. variables is finite, the attractor distribution is the normal distribution. In contrast, the sum of a number of i.i.d. random variables with power law tail distributions decreasing as |x|−α−1 where 0 < α < 2 (and therefore having infinite variance) will tend to an alpha-stable distribution with stability parameter (or index of stability) of α as the number of variables grows.".
• Central_limit_theorem thumbnail Central_limit_thm.png?width=300.
• Central_limit_theorem wikiPageExternalLink prob:central_limit_theorem.
• Central_limit_theorem wikiPageExternalLink 0705.0832.
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• Central_limit_theorem wikiPageExternalLink TheCentralLimitTheorem.
• Central_limit_theorem wikiPageExternalLink MIT18_440S11_Lecture31.pdf.
• Central_limit_theorem wikiPageExternalLink About_pages_for_SOCR_Experiments.
• Central_limit_theorem wikiPageExternalLink SOCR_EduMaterials_Activities_GeneralCentralLimitTheorem.
• Central_limit_theorem wikiPageExternalLink dinov.html.
• Central_limit_theorem wikiPageExternalLink www.causeweb.org.
• Central_limit_theorem wikiPageExternalLink ExcelSampler.
• Central_limit_theorem wikiPageExternalLink SOCR_Experiments.html.
• Central_limit_theorem wikiPageExternalLink central_limit_theorem.html.
• Central_limit_theorem wikiPageExternalLink simusoft_cenlimit.html.
• Central_limit_theorem wikiPageID "39406".
• Central_limit_theorem wikiPageRevisionID "645380662".
• Central_limit_theorem date "April 2012".
• Central_limit_theorem date "June 2012".
• Central_limit_theorem hasPhotoCollection Central_limit_theorem.
• Central_limit_theorem id "p/c021180".
• Central_limit_theorem reason "give source for this style of notation, else write using indicator functions".
• Central_limit_theorem reason "what does up to mean here".
• Central_limit_theorem title "Central Limit Theorem".
• Central_limit_theorem title "Central limit theorem".
• Central_limit_theorem urlname "CentralLimitTheorem".
• Central_limit_theorem subject Category:Articles_containing_proofs.
• Central_limit_theorem subject Category:Asymptotic_statistical_theory.
• Central_limit_theorem subject Category:Central_limit_theorem.
• Central_limit_theorem subject Category:Probability_theorems.
• Central_limit_theorem subject Category:Statistical_terminology.
• Central_limit_theorem subject Category:Statistical_theorems.
• Central_limit_theorem type Abstraction100002137.
• Central_limit_theorem type Communication100033020.
• Central_limit_theorem type Message106598915.
• Central_limit_theorem type ProbabilityTheorems.
• Central_limit_theorem type Proposition106750804.
• Central_limit_theorem type Statement106722453.
• Central_limit_theorem type StatisticalTheorems.
• Central_limit_theorem type Theorem106752293.
• Central_limit_theorem comment "In probability theory, the central limit theorem (CLT) states that, given certain conditions, the arithmetic mean of a sufficiently large number of iterates of independent random variables, each with a well-defined expected value and well-defined variance, will be approximately normally distributed, regardless of the underlying distribution.".
• Central_limit_theorem label "Central limit theorem".
• Central_limit_theorem label "Centrale limietstelling".
• Central_limit_theorem label "Centralne twierdzenie graniczne".
• Central_limit_theorem label "Centrális határeloszlás-tétel".
• Central_limit_theorem label "Centrální limitní věta".
• Central_limit_theorem label "Limitearen teorema zentral".
• Central_limit_theorem label "Merkezi limit teoremi".
• Central_limit_theorem label "Teorema central do limite".
• Central_limit_theorem label "Teorema del límit central".
• Central_limit_theorem label "Teorema del límite central".
• Central_limit_theorem label "Teorema limit pusat".
• Central_limit_theorem label "Teoremi centrali del limite".
• Central_limit_theorem label "Théorème central limite".
• Central_limit_theorem label "Zentraler Grenzwertsatz".
• Central_limit_theorem label "Центральная предельная теорема".
• Central_limit_theorem label "中心極限定理".
• Central_limit_theorem label "중심극한정리".
• Central_limit_theorem sameAs Centrální_limitní_věta.
• Central_limit_theorem sameAs Zentraler_Grenzwertsatz.
• Central_limit_theorem sameAs Θεώρημα_κεντρικού_ορίου.
• Central_limit_theorem sameAs Teorema_del_límite_central.
• Central_limit_theorem sameAs Limitearen_teorema_zentral.
• Central_limit_theorem sameAs Théorème_central_limite.
• Central_limit_theorem sameAs Teorema_limit_pusat.
• Central_limit_theorem sameAs Teoremi_centrali_del_limite.
• Central_limit_theorem sameAs 中心極限定理.
• Central_limit_theorem sameAs 중심극한정리.
• Central_limit_theorem sameAs Centrale_limietstelling.
• Central_limit_theorem sameAs Centralne_twierdzenie_graniczne.
• Central_limit_theorem sameAs Teorema_central_do_limite.
• Central_limit_theorem sameAs m.09t70.
• Central_limit_theorem sameAs Q190391.
• Central_limit_theorem sameAs Q190391.
• Central_limit_theorem sameAs Central_limit_theorem.
• Central_limit_theorem wasDerivedFrom Central_limit_theorem?oldid=645380662.
• Central_limit_theorem depiction Central_limit_thm.png.
• Central_limit_theorem isPrimaryTopicOf Central_limit_theorem.