泊松分布

X~P{X=K}=概率质量函数

P(X=k) =$\frac{\lambda^k e^{-\lambda}}{k!},\quad
k=0,1,2,\dots (\lambda>0) $
(1)$\ p_k \ge 0, \$

(2)$\ \sum_{k=0}^{\infty} p_k = \sum_{k=0}^{\infty} \frac{\lambda^k}{k!} e^{-\lambda} = e^{-\lambda} \sum_{k=0}^{\infty} \frac{\lambda^k}{k!} = e^{-\lambda} \cdot e^{\lambda} = 1$

$二项分布->泊松分布X~B(n,p)$
$n>=100 p小 np<=10 \lambda=np$

几何分布

$P(X=k) = q^{k-1}p,\quad k=1,2,3,\dots$

$(1)\ p_k \ge 0, \$
$(2)\ \sum_{k=1}^{\infty} p_k = \sum_{k=1}^{\infty} (1-p)^{k-1} p = \frac{p}{1-(1-p)} = 1$

超几何分布

二、概率质量函数

$P(X=k) = \frac{\mathrm{C}M^k \cdot \mathrm{C}{N-M}^{n-k}}{\mathrm{C}_N^n}, \quad k = 0,1,2,\dots,\min(n,M)$
$N很大，n对N较小约等于P(X=k) = \mathrm{C}_n^k p^k (1-p)^{n-k}, \quad k=0,1,2,\dots,n$