15.2.8 One dimensional random variables and their characteristics

Problem: The random variable \( \xi \) is given by the density of the distribution \( P_{\xi}(x) \). The random variable \( \eta \) is the area of a regular triangle with side \( \xi \). For the random variable \( \eta \) find the distribution function, the density of the distribution, the expected value and the dispersion, where \[ \begin{array}{l} P_{\xi}(x)=\left\{\begin{array}{l} \frac{2(x-a)}{(b-a)^{m}}, \quad x \in[a, b], \\ 0, \quad x \notin[a, b] \end{array}\right. \\ a=2, \quad b=4, \quad m=2 . \end{array} \]