Hypergeometric distribution convergences binomial distribution

294 Views Asked by At

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?