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Consider the central limit theorem for independent Bernoulli random variables ... , where ... and ... , ... . Then the sum ... is binomial with parameters ... and ... and ... converges in distribution to the standard normal. The exact distribution for ... may be written ... , where ... , ... , ... . The convergence may be illustrated using rectangles of width ... and height ... centered at ... . As ... increases, the rectangles closely approach the standard normal density function. The convergence is faster in the symmetric case when ... .

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      EUN,LOM,LRE4,work-cmr-id:396979,http://demonstrations.wolfram.com:http://demonstrations.wolfram.com/IllustratingTheCentralLimitTheoremWithSumsOfBernoulliRandomV/,ilox,learning resource exchange,LRE metadata application profile,LRE

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