463. Find the sample variance for the given sample distribution of size $n=10$:

$$
\begin{array}{cccc}
x_{i} & 0.01 & 0.04 & 0.08 \\
n_{i} & 5 & 3 & 2
\end{array}
$$
Solution. To avoid operations with fractions, we will switch to conditional variants $u_{i}=100 x_{i}$. As a result, we will get the distribution

$$
\begin{array}{llll}
u_{i} & 1 & 4 & 8 \\
n_{i} & 5 & 3 & 2
\end{array}
$$

We will find the sample variance of the conditional variants:

$$
D_{\mathrm{B}}(u)=\left(\sum n_{i} u_{i}^{2}\right) / n-\left[\left(\sum n_{i} u_{i}\right)_{i}^{\prime} n\right]^{2}
$$

Substituting the conditional variants and their frequencies into this formula, we get

$$
D_{\mathrm{B}}(u)=7.21 .
$$

We will find the required sample variance of the original variants:

$$
D_{\mathrm{B}}(X)=D_{\mathrm{B}}(u) / 100^{2}=7.21 / 10000=0.0007
$$