Example 5. The distribution law of a discrete random variable is given by the following table:

| $X$ | 0 | 1 | 2 | 3 |
| :---: | :---: | :---: | :---: | :---: |
| $P$ | 0.2 | 0.4 | 0.3 | 0.1 |

Find the distribution function of this random variable.
Solution. To construct the distribution function $F(x)$ of a discrete random variable $X$, we use formula (2.2.11).

1. For $x \leq 0 \quad F(x)=\sum_{x_{k}3 \quad F(x)=P(X=0)+P(X=1)+P(X=2)+P(X=3)=$

$$
=0.2+0.4+0.3+0.1=1
$$

The graph of the function $F(x)$ is shown in Fig. 2.7.