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77julia77 [94]
4 years ago
5

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

etric distribution:
Mathematics
1 answer:
sasho [114]4 years ago
6 0

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

Let

<span><span>f(x)=<span><span><span>(<span>rx</span>)</span><span>(<span><span>N−r</span><span>n−x</span></span>)</span></span><span>(<span>Nn</span>)</span></span>,</span><span>f(x)=<span><span><span>(<span>rx</span>)</span><span>(<span><span>N−r</span><span>n−x</span></span>)</span></span><span>(<span>Nn</span>)</span></span>,</span></span>and keep <span><span>p=<span>rN</span></span><span>p=<span>rN</span></span></span> fixed. Prove that<span><span><span>lim<span>N→∞</span></span>f(x)=<span>(<span>nx</span>)</span><span>px</span>(1−p<span>)<span>n−x</span></span>.</span><span><span>lim<span>N→∞</span></span>f(x)=<span>(<span>nx</span>)</span><span>px</span>(1−p<span>)<span>n−x</span></span>.</span></span>

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


Anyway... I hoped this helped!

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