408. The probability distribution of a discrete two-dimensional random variable is given:

| $y$ | $x$ |  |  |
| :---: | :---: | :---: | :---: |
|  | 3 | 10 | 12 |
|  |  |  |  |
| 4 | 0.17 | 0.13 | 0.25 |
| 5 | 0.10 | 0.30 | 0.05 |

Find the distribution laws of the components $X$ and $Y$.
Solution. By summing the probabilities "by columns", we obtain the probabilities of possible values of $X: p(3)=0.27, p(10)=0.43, p(12)=0.30$. We write the distribution law of the component $X$:

$$
\begin{array}{ccccc}
X & 3 & 10 & 12 \\
p & 0.27 & 0.43 & 0.30
\end{array}
$$

Check: $0.27+0.43+0.30=1$.

By summing the probabilities "by rows", we similarly find the distribution of the component $Y$:

| $Y$ | 4 | 5 |
| :---: | :---: | :---: |
| $p$ | 0.55 | 0.45 |

Check: $0.55+0.45=1$.