Discrete random variables and their distribution columns

This section has the following main contents:

(1) Discrete random variables

If the result of a randomized trial can be represented by a variable, then such a variable is called a random variable . The random variables that all values can be listed are called discrete random variables .

(2) Distribution columns of discrete random variables

Generally, if the discrete random variable $x$ may take different values of $x_1$, $x _2$, ..., $x _i$, ..., $x _n$, $X $ take each value $x_i$ ($i =1$,$2$, ..., $n $) The probability $p (x=x_i) =p_i$, in tabular form as follows:

$X $	$x _1$	$x _2$	....	$x _i$		$x _n$
$P $	$p _1$	$p _2$	...	$p _i$	...	$p _n$

The table is the Probability distribution column (probability distribution series) of the discrete random variable $x$, which is referred to as the distribution column of $x$ (distribution series).
Sometimes for the sake of simplicity, we also use the equation
\begin{equation*}
P (x=x_i) =p_i, I=1, 2, ..., n
\end{equation*}
Represents a distribution column for $x$.

(3) Properties of distributed columns of discrete random variables

Discrete random variables and their distribution columns