15.5.12 Two-dimensional random variables and their characteristics

Problem: Is it possible to make a distribution table of the random vector \( \eta_{1}=\left(\tau_{1}, \tau_{2}\right)^{T} \), where \( \tau_{1}=2 \xi_{1}- \) \( -3 \xi_{2}+4, \tau_{2}=\xi_{1}^{\xi_{2}} \), if the distribution table of the discrete random vector \( \eta=\left(\xi_{1}, \xi_{2}\right)^{T} \) is known? \begin{tabular}{|c|c|c|c|} \hline\( y_{j} \) & 0 & 1 & 2 \\ \hline\( x_{i} \) & & & \\ \hline-1 & 0.1 & 0.2 & 0.3 \\ \hline 1 & 0.2 & 0.1 & 0.1 \\ \hline \end{tabular} Find, if it's possible under the given complex of conditions, the expected value of the vector \( E\left[\eta_{1}\right] \) and the covariance of the matrix \( V_{\eta_{1}} \).