Example 8. The random variable $X$ is given by the distribution function

$$
F(x)=\left\{\begin{array}{lc}
0 & \text { if } x \leq 0 \\
x / 3 & \text { if } 0 < x \leq 3 \\
1 & \text { if } x > 3
\end{array}\right.
$$

Find the probability that in the result of the trial, the variable $X$ will take a value from the interval $(2,3)$.
Solution. By formula (2.2.2), we find:

$$
P(2<x \leq 3)=F(3)-F(2)=(3 / 3)-(2 / 3)=1-2 / 3=1 / 3 .
$$