96. Let $X$ be the number of points that fall when a die is rolled once. Find the variance of the random variable $X$.
Solution. The distribution law of the random variable $X$ and its mathematical expectation $M(X)=3.5$ were found in the previous example. Let's find the deviations for $x_{1}, x_{2}, \ldots, x_{6}$:

$$
\begin{aligned}
x_{1}^{0}=1-3.5 ; x_{2}^{0}=2-3.5 ; x_{3}^{0} & =3-3.5 ; x_{9}^{0}=4-3.5 ; x_{5}^{0}=5-3.5 ; \\
x_{6}^{0} & =6-3.5 .
\end{aligned}
$$

Let's compute the variance:

$$
\begin{gathered}
D(x)=\frac{1}{6}\left[(1-3.5)^{2}+(2-3.5)^{2}+(3-3.5)^{2}+(4-3.5)^{2}+(5-3.5)^{2}+\right. \\
\left.+(6-3.5)^{2}\right]=\frac{35}{12}
\end{gathered}
$$