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The hypergeometric distribution can be approximated by either the binomial or the poisson distribution. let x have the hypergeometric distribution:

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jpGymnastics7Books

I have this problem on a textbook that doesn't have a solution. It is:

Let

f(x)=(rx)(N−rn−x)(Nn),f(x)=(rx)(N−rn−x)(Nn),and keep p=rNp=rN fixed. Prove thatlimN→∞f(x)=(nx)px(1−p)n−x.limN→∞f(x)=(nx)px(1−p)n−x.

Although I can find lots of examples using the binomial to approximate the hypergeometric for very large values of NN, I couldn't find a full proof of this online.


Anyway... I hoped this helped!

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