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I don't understand the following statement: Let $X_N$ , N $=$ 1,2, ... random variables with hypergeometric distribution; Parameter ($N$,[P$N$],n).

Show that:

$$\lim_{N\to \infty} P( X_N = k ) = \binom{n}{k} p^k (1-p)^{n-k}$$

Does this means that the hypergeometric distribution approaches binomial distribution for N $\rightarrow$ $\infty$ ?

Can somebody give me only the beginning of this proof?

Leucippus
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Mugumble
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  • I would suggest to read the first line of this https://math.stackexchange.com/q/330553/349501 – Shashi Nov 18 '17 at 00:14
  • And that is also a possible duplicate – Shashi Nov 18 '17 at 00:15
  • Oh I didn't found that. I'm sorry. Thank you very much. But I have one more question: In the other post they fixed p=$r/N$. I have [P$N$]. What is the difference? – Mugumble Nov 18 '17 at 13:17
  • do you mean the integer part of $pN$? – Shashi Nov 18 '17 at 13:23
  • yes. I don't understand why we consider the integer part of pN instead of a fixed p with p=r/N. – Mugumble Nov 18 '17 at 23:44
  • there is no big difference. You could also say set $p=r/N$ fixed and then you would have $[pN]=[r]$ and the calculations would remain (almost) the same. – Shashi Nov 19 '17 at 00:02

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