다항분포 (Multinomial Distribution)

$$ X \sim MN(n;p_{1}, ... ,p_{k})$$

$$p(x_{1}, \ \cdots \ , x_{k})=\frac{n!}{x_{1}! \ \cdots \ x_{k}!}p_{1}^{x_{1}} \ \cdots \ p_{k}^{x_{k}} , (x_{1}+ \ \cdots \ + x_{n} =n)$$

$$E(X)=n_{i}p_{i}$$

$$Var(X)=n_{i}p_{i}(1-p_{i})$$

$$M(t)=(p_{1}e^{t_{1}}+ ... +p_{k-1}e^{t_{k-1}}+ ... +p_{k})^{n}$$

• 분포