| 31. | Two representative mathematical results describing such patterns are the law of large numbers and the central limit theorem.
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| 32. | A simple example of the central limit theorem is rolling a large number of identical, unbiased dice.
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| 33. | While at UNC, Lacey and Walter Philipp gave their proof of the almost sure central limit theorem.
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| 34. | And because of the Central limit theorem, bell curves pop up all over the place in nature.
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| 35. | This example serves to show that the hypothesis of finite variance in the central limit theorem cannot be dropped.
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| 36. | For large sample sizes, the central limit theorem says this distribution tends toward a certain multivariate normal distribution.
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| 37. | Also, the distribution of the mean is known to be asymptotically normal due to the central limit theorem.
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| 38. | The non-Gaussianity family of ICA algorithms, motivated by the central limit theorem, uses kurtosis and negentropy.
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| 39. | :" Regularisation " principles in statistics and probability include the law of large numbers and the central limit theorem.
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| 40. | Largely because of the central limit theorem, the standard normal distribution plays a fundamental role in probability theory and statistics.
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