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This is not the Central Limit Theorem.
by coherentpony 13y ago
This is not the Central Limit Theorem.
- dietrichepp 13y agoReally? I see a collection X1, X2, ..., XN of Bernoulli(0.5) variables and the demonstration that the distribution of their sum, normalized for variance, approaches the Gaussian distribution as N increases. Is that not a direct consequence of the CLT?
- jonahx 13y agowhat do you mean by "normalized for variance"?
- zmmmmm 13y ago> the distribution of their sum Exactly. But the page defines the CLT as referring to: "the mean of a sufficiently large number of independent random variables ..." So it talks about the mean and then illustrates the sum, just as you are, which is confusing. I spent several minutes puzzling about how the mean of variables between zero and 1 could be 5, for example. Now, I suppose you will say, the distribution of the mean is just the distribution of the sum, normalized, and this ought to be obvious to anybody with half a brain, but if this page is meant to help people trying to learn this stuff understand it, it would be better if it was accurate and not directly confusing with its language.
- coherentpony 13y agoNo, it is a property of Bernoulli trials. The distribution is a Binomial distribution, not a Normal distribution. They do, however, look similar http://en.wikipedia.org/wiki/File:Binomial_Distribution.svg http://en.wikipedia.org/wiki/File:Binomial_Distribution.svg