Central limit theorem: Difference between revisions

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It states formally that the average of a large number of independent identically distributed random variables will have a normal distribution.
''Financial maths.''
 
The central limit theorem states formally that the average of a large number of independent identically distributed random variables will have a normal distribution.
 
 
The central limit theorem is important in sampling theory. 
 
It explains that sample means follow a normal distribution - regardless of the actual distribution of the parent population - and that the sample mean is an unbiased estimate of the parent population mean.


The central limit theorem is important in sampling theory.  It explains that sample means follow a normal distribution - regardless of the actual distribution of the parent population - and that the sample mean is an unbiased estimate of the parent population mean.


The central limit theorem also explains why larger samples will - on average - produce better estimates of the parent population mean.
The central limit theorem also explains why larger samples will - on average - produce better estimates of the parent population mean.


The central limit theorem is sometimes known as the '' law of large numbers''.   
The central limit theorem is sometimes known as the '' law of large numbers''.   


== See also ==
== See also ==
* [[Mean]]
* [[Normal frequency distribution]]
* [[Sample]]
* [[Sample]]
* [[Sampling]]
* [[Sampling]]


[[Category:The_business_context]]
[[Category:Identify_and_assess_risks]]

Latest revision as of 20:54, 1 July 2022

Financial maths.

The central limit theorem states formally that the average of a large number of independent identically distributed random variables will have a normal distribution.


The central limit theorem is important in sampling theory.

It explains that sample means follow a normal distribution - regardless of the actual distribution of the parent population - and that the sample mean is an unbiased estimate of the parent population mean.


The central limit theorem also explains why larger samples will - on average - produce better estimates of the parent population mean.


The central limit theorem is sometimes known as the law of large numbers.


See also