15.5.9 Two-dimensional random variables and their characteristics

Problem: The distribution table of the discrete random vector \( \eta=\left(\xi_{1}, \xi_{2}\right)^{T} \) is given: \begin{tabular}{|c|c|c|c|} \hline\( y_{j} \) & -1 & 0 & 1 \\ \hline\( x_{i} \) & & & \\ \hline-1 & \( 1 / 8 \) & \( 1 / 12 \) & \( 7 / 24 \) \\ \hline 1 & \( 5 / 24 \) & \( 1 / 6 \) & \( 1 / 8 \) \\ \hline \end{tabular} 1) Find the marginal laws of distribution for random variables \( \xi_{1} \) and \( \xi_{2} \). 2) Calculate \( E\left[\xi_{1} / \xi_{2}\right] \) and \( E\left[\xi_{2} / \xi_{1}=1\right] \). 3) Make the distribution tables of random variables \( \tau_{1}=\xi_{1} \xi_{2} \) and \( \tau_{2}=\xi_{1}+\xi_{2} \).