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Statistics
Convergence and the central Limit Theorem
(m23475)
Author:
Paul E Pfeiffer
Keywords:
Convergence of sequences of random variables
,
Relationships between types of convergence
,
Weak law of large numbers
Summary:
The central limit theorem (CLT) asserts that the sum of a large class of independent random variables, each with reasonable distributions,is approximately normally distributed. Various versions of this theorem have been studied intensively. On the other hand, certain common forms serve as the basis of an extraordinary amount of ... quite appropriate
[Expand Summary]
The central limit theorem (CLT) asserts that the sum of a large class of independent random variables, each with reasonable distributions,is approximately normally distributed. Various versions of this theorem have been studied intensively. On the other hand, certain common forms serve as the basis of an extraordinary amount of applied work. In the statistics of large samples, the sample average is approximately normalâ€”whether or not the population distribution is normal. In much of the theory of errors of measurement, the observed error is the sum of a large number of independent random quantities which contribute additively to the result. Similarly, in the theory of noise, the noise signal is the sum of a large number of random components, independently produced. In such situations, the assumption of a normal population distribution is frequently quite appropriate
[Collapse Summary]
Subject:
Mathematics and Statistics
Language:
English
Popularity:
80.95%
Revised:
20090918
Revisions:
6
Popularity is measured as percentile rank of page views/day over all time
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