Probability Distributions

probability of $k$ successes in a sample of size $n$ drawn without replacement from a finite population of size $N$ that contains exactly $K$ successes.

N개 중 K개의 event가 있는 모집단에서, n개의 샘플을 뽑았을 때 event 가 k번 일어나는 확률

$X \sim \text{Hypergeom}(N, K, n)$
$$P(X = k) = \frac{{K \choose k}{N-K \choose n-k}}{N \choose n}$$

$$ N