概率分布律

PMF Probability mass function
概率分布列/概率质量函数

每个离散的点对应的概率

\begin{aligned} P {X = x_{i}} = p (x_{i}) = p_{i} i = 1, 2, \dots \end{aligned}

分布列的性质

P (x_{i}) \geq 0, i = 1, 2, \dots

\sum_{i = 1}^{\infty} p (x_{i}) = 1

分布函数为 $F (x) = \sum_{x_{i} \leq x} p (x_{i})$ ，

例子：

F (x) = {\begin{cases} 0 & x < 0 \\ \frac{1}{2} & 0 \leq x < 1 \\ \frac{1}{2} + \frac{1}{4} = \frac{3}{4} & 1 \leq x < 2 \\ \frac{1}{2} + \frac{1}{4} + \frac{1}{8} = \frac{7}{8} & 2 \leq x < 3 \\ \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{8} = 1 & x \geq 3 \end{cases}