Last modified on November 27, 2015, at 03:37

Talk:Central limit theorem

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The distribution of an average of samples, taken from any' type of underlying probability function, will approach a Normal distribution as the sample size increases

The distribution of an average of samples taken from a standard Cauchy distribution will approach the Cauchy distribution. Do you see the problem, Andy? --AugustO (talk) 14:31, 26 November 2015 (EST)

No, I don't see a problem. For a sample size of one, you are correct. For a sample size of infinity, all the averages equal the average of the original Cauchy distribution. As the sample size goes from small to large, the distribution of the averages is the Normal distribution.--Andy Schlafly (talk) 15:33, 26 November 2015 (EST)
No, sorry, the theorem doesn't hold for the Cauchy distribution: doesn't matter, how large the sample size is, the average of a number of Cauchy distributed random variables will be the Cauchy distributed... --AugustO (talk) 15:55, 26 November 2015 (EST)
Great point about a rare exception. Problem fixed by adding the condition for a finite variance to the definition. Thanks.--Andy Schlafly (talk) 22:37, 26 November 2015 (EST)