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Chi-Squared Distribution and the Central Limit Theorem


	This Demonstration explores the chi-squared distribution for large degrees of freedom , which, when suitably standardized, approaches a standard normal distribution as by the central limit theorem. In this Demonstration, can be varied between 1 and 2000 and either the PDF or CDF of the chi-squared and standard normal distribution can be viewed. You can also see the difference between the two distributions, which becomes useful for large .


	Contributed by: Peter Falloon
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are independent standard normal variables, then the random variable

follows the chi-squared distribution with mean

and standard deviation

. Taking the standardized variable

, the central limit theorem implies that the distribution of

tends to the standard normal distribution as

It can be seen that the chi-squared distribution is skewed, with a longer tail to the right. However, the PDF has maximum value at

(for

), which is equivalent to

, so the skew disappears in the limit as

Contributed by: Peter Falloon

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