Question

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

Answer 1

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!