MONT 105Q -- Mathematical Journeys 

Probability Histograms -- Evidence for CLT 

February 5, 2010 

Consider the box  and make  draws with replacement.  
What do the probability histograms look like as  increases?   

Here is some code (for the computer algebra system Maple we use in 

many mathematics courses) in that computes the binomial probabilities 

and generates the corresponding probability histograms: 

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With  draws: 

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With  draws: 

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With  draws: 

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With  draws  (at this point, notice that
the probability histogram is starting to look more "normal"
in shape(!)
 

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Finally, with  draws, and an approximating
normal curve in red:
 

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