Talk:Central limit theorem - Revision history

Aschlafly: Great point about a rare exception. Problem fixed by adding the condition for a finite variance to the definition. Thanks.

2015-11-27T03:37:44Z

Great point about a rare exception. Problem fixed by adding the condition for a finite variance to the definition. Thanks.

AugustO at 20:56, November 26, 2015

2015-11-26T20:56:33Z

AugustO at 20:55, November 26, 2015

2015-11-26T20:55:16Z

Aschlafly: 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.

2015-11-26T20:33:55Z

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.

AugustO: Created page with "==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 d..."

2015-11-26T19:31:30Z

Created page with "==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 d..."

New page

==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? --[[User:AugustO|AugustO]] ([[User talk:AugustO|talk]]) 14:31, 26 November 2015 (EST)

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	::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... --[[User:AugustO\|AugustO]] ([[User talk:AugustO\|talk]]) 15:55, 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... --[[User:AugustO\|AugustO]] ([[User talk:AugustO\|talk]]) 15:55, 26 November 2015 (EST)
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		+	:::Great point about a rare exception. Problem fixed by adding the condition for a finite variance to the definition. Thanks.--[[User:Aschlafly\|Andy Schlafly]] ([[User talk:Aschlafly\|talk]]) 22:37, 26 November 2015 (EST)

← Older revision		Revision as of 20:56, November 26, 2015
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	: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]].--[[User:Aschlafly\|Andy Schlafly]] ([[User talk:Aschlafly\|talk]]) 15:33, 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]].--[[User:Aschlafly\|Andy Schlafly]] ([[User talk:Aschlafly\|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 ~~distribution~~ will be the Cauchy ~~distribution~~... --[[User:AugustO\|AugustO]] ([[User talk:AugustO\|talk]]) 15:55, 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... --[[User:AugustO\|AugustO]] ([[User talk:AugustO\|talk]]) 15:55, 26 November 2015 (EST)

← Older revision		Revision as of 20:55, November 26, 2015
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	: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]].--[[User:Aschlafly\|Andy Schlafly]] ([[User talk:Aschlafly\|talk]]) 15:33, 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]].--[[User:Aschlafly\|Andy Schlafly]] ([[User talk:Aschlafly\|talk]]) 15:33, 26 November 2015 (EST)
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		+	::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 distribution will be the Cauchy distribution... --[[User:AugustO\|AugustO]] ([[User talk:AugustO\|talk]]) 15:55, 26 November 2015 (EST)

← Older revision		Revision as of 20:33, November 26, 2015
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	The distribution of an average of samples taken from a standard Cauchy distribution will approach the Cauchy distribution. Do you see the problem, Andy? --[[User:AugustO\|AugustO]] ([[User talk:AugustO\|talk]]) 14:31, 26 November 2015 (EST)		The distribution of an average of samples taken from a standard Cauchy distribution will approach the Cauchy distribution. Do you see the problem, Andy? --[[User:AugustO\|AugustO]] ([[User talk: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]].--[[User:Aschlafly\|Andy Schlafly]] ([[User talk:Aschlafly\|talk]]) 15:33, 26 November 2015 (EST)