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Student Support Forum: 'Binomial Distribution Limits' topicStudent Support Forum > General > "Binomial Distribution Limits"

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Tom
12/26/09 6:02pm

Hi,

According to http://en.wikipedia.org/wiki/Binomial_distribution and http://mathworld.wolfram.com/BinomialDistribution.html , it seems like the following should evaluate to True:

FullSimplify[
Limit[FunctionExpand@PDF[BinomialDistribution[n, p], x],
n -> Infinity] ==
PDF[NormalDistribution[n p, Sqrt[n p (1 - p)]],
x], (n | x) \[Element] Integers && n >= 0 && 0 <= p <= 1 &&
p \[Element] Reals && x <= n && x >= 0]

I added all the assumptions I can think of, but it still doesn't evaluate. Am I making a mistake, or is Mathematica missing this identity?

Thanks,
Tom

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