Finite Math Examples

A discrete random variable ${\displaystyle x}$ takes a set of separate values (such as ${\displaystyle 0}$, ${\displaystyle 1}$, ${\displaystyle 2}$...). Its probability distribution assigns a probability ${\displaystyle P\left(x\right)}$ to each possible value ${\displaystyle x}$. For each ${\displaystyle x}$, the probability ${\displaystyle P\left(x\right)}$ falls between ${\displaystyle 0}$ and ${\displaystyle 1}$ inclusive and the sum of the probabilities for all the possible ${\displaystyle x}$ values equals to ${\displaystyle 1}$.

${\displaystyle \frac{1}{3}}$ is between ${\displaystyle 0}$ and ${\displaystyle 1}$ inclusive, which meets the first property of the probability distribution.

${\displaystyle 1}$ is between ${\displaystyle 0}$ and ${\displaystyle 1}$ inclusive, which meets the first property of the probability distribution.

${\displaystyle 3}$ is not less than or equal to ${\displaystyle 1}$, which doesn't meet the first property of the probability distribution.

${\displaystyle 9}$ is not less than or equal to ${\displaystyle 1}$, which doesn't meet the first property of the probability distribution.

${\displaystyle 27}$ is not less than or equal to ${\displaystyle 1}$, which doesn't meet the first property of the probability distribution.

The probability ${\displaystyle P\left(x\right)}$ does not fall between ${\displaystyle 0}$ and ${\displaystyle 1}$ inclusive for all ${\displaystyle x}$ values, which does not meet the first property of the probability distribution.