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| URL | https://www.britannica.com/science/probability-theory/The-central-limit-theorem | |||||||||
| Last Crawled | 2026-04-03 23:36:53 (2 months ago) | |||||||||
| First Indexed | 2018-02-19 19:49:50 (8 years ago) | |||||||||
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| Meta Title | Probability theory - Central Limit, Statistics, Mathematics | Britannica | |||||||||
| Meta Description | Probability theory - Central Limit, Statistics, Mathematics: The desired useful approximation is given by the central limit theorem, which in the special case of the binomial distribution was first discovered by Abraham de Moivre about 1730. Let X1,…, Xn be independent random variables having a common distribution with expectation μ and variance σ2. The law of large numbers implies that the distribution of the random variable X̄n = n−1(X1 +⋯+ Xn) is essentially just the degenerate distribution of the constant μ, because E(X̄n) = μ and Var(X̄n) = σ2/n → 0 as n → ∞. The standardized random variable (X̄n − μ)/(σ/n) has mean 0 and variance | |||||||||
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| Language | en | |||||||||
| Author | David O. Siegmund | |||||||||
| Publish Time | 2026-03-01 00:00:00 (3 months ago) | |||||||||
| Original Publish Time | 2018-02-19 19:49:50 (8 years ago) | |||||||||
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