Task 1. A discrete random variable $X$ takes possible values $1,2,3,4$ with probabilities respectively 0.25, 0.35, 0.3, and $p$. Find $p$, construct the distribution table, and plot the distribution polygon.
Solution. The number $p$ is found from the condition $0.25+0.35+0.3+p=1$. We get $p=0.1$. The polygon is shown in Fig. 7.2, and the table is as follows:

| $X$ | 1 | 2 | 3 | 4 | $\Sigma$ |
| :---: | :---: | :---: | :---: | :---: | :---: |
| $p$ | 0.25 | 0.35 | 0.3 | 0.1 | 1 |

![](https://cdn.mathpix.com/cropped/2024_05_22_446938f1e4808e7d6e07g-151.jpg?height=212&width=343&top_left_y=1559&top_left_x=2137)

Fig. 7.2