有限数学 示例

取自独立值集合（例如 ${\displaystyle 0}$、${\displaystyle 1}$、${\displaystyle 2}$……）的离散随机变量 ${\displaystyle x}$。其概率分布将概率 ${\displaystyle x}$ 赋值给每一个可能值 ${\displaystyle P\left(x\right)}$。对于每一个 ${\displaystyle x}$，概率 ${\displaystyle P\left(x\right)}$ 介于 ${\displaystyle 0}$（含）和 ${\displaystyle 1}$（含）之间，且所有可能 ${\displaystyle x}$ 值的概率之和等于 ${\displaystyle 1}$。

${\displaystyle 3}$ 不小于或等于 ${\displaystyle 1}$，即不符合概率分布的第一个性质。

${\displaystyle 2}$ 不小于或等于 ${\displaystyle 1}$，即不符合概率分布的第一个性质。

${\displaystyle 1}$ 介于 ${\displaystyle 0}$（含）和 ${\displaystyle 1}$ （含）之间，符合概率分布的第一个性质。

${\displaystyle 0}$ 介于 ${\displaystyle 0}$（含）和 ${\displaystyle 1}$ （含）之间，符合概率分布的第一个性质。

${\displaystyle -1}$ is not greater than or equal to ${\displaystyle 0}$, which doesn't meet the first property of the probability distribution.

${\displaystyle -2}$ is not greater than or equal to ${\displaystyle 0}$, which doesn't meet the first property of the probability distribution.

${\displaystyle -3}$ is not greater than or equal to ${\displaystyle 0}$, which doesn't meet the first property of the probability distribution.

对于所有 ${\displaystyle x}$ 值，概率 ${\displaystyle P\left(x\right)}$ 不介于 ${\displaystyle 0}$（含）和 ${\displaystyle 1}$（含）之间，即不满足概率分布的第一条性质。