Does anyone know anything about the Central Limit Theorem?

Question

For Stats?
Do you know of any sites or anything that explains it....thanks

THANKS to everyone so far!!

Answer 1

A central limit theorem is any of a set of weak-convergence results in probability theory. They all express the fact that any sum of many independent and identically-distributed random variables will tend to be distributed according to a particular "attractor distribution". The most important and famous result is called The Central Limit Theorem which states that if the sum of the variables has a finite variance, then it will be approximately normally distributed (i.e. following a normal or Gaussian distribution).

Since many real processes yield distributions with finite variance, this explains the ubiquity of the normal probability distribution.

Several generalizations for finite variance exist which do not require identical distribution but incorporate some condition which guarantees that none of the variables exert a much larger influence than the others. Two such conditions are the Lindeberg condition and the Lyapunov condition. Other generalizations even allow some "weak" dependence of the random variables. Also, a generalization due to Gnedenko and Kolmogorov states that the sum of a number of random variables with power-law tail distributions decreasing as 1/|x|α+1 with 0 < α < 2 (and therefore having infinite variance) will tend to a symmetric stable Lévy distribution as the number of variables grows. This article will only be concerned with the central limit theorem as it applies to distributions with finite variance.

Hope that helps. =)

Answer 2

A quick Google ... three sources that appear to be at least "OK"

http://en.wikipedia.org/wiki/Central_limit_theorem

http://www.statisticalengineering.com/central_limit_theorem.htm

http://www.intuitor.com/statistics/CentralLim.html

Answer 3

http://en.wikipedia.org/wiki/Central_limit_theorem

Answer 4

Try this site.

http://mathworld.wolfram.com/CentralLimitTheorem.html