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MATH 375 -- Probability and Statistics 1 

Central Limit Theorem Demonstration 

December 1, 2009 

We consider the distribution of the means of  

random samples of size  n  from a given distribution, 

described by a given pdf   

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First, let's consider a uniform distribution on the interval from 2 to 4, and  The procedure MP 

takes 300 random samples of size 100 from this distribution and plots a histogram of the means. 

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(1)

 

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Second, let's do the same sort of experiment with an exponential distribution. 

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(2)

 

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Next let's take a rather different-looking pdf:
 

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(3)

 

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(4)

 

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Again, we take random samples of size  n  from this distribution and 

plot a histogram of their means.  As  n  increases, note how the distribution 

of the sample means becomes closer and closer to a normal(!) 

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(5)

 

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(6)

 

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