15.5.11 Two-dimensional random variables and their characteristics

Problem: Find the law of distribution of the random variable \( \tau=\left|\xi_{1}-\xi_{2}\right| \), if 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\( y_{j} \) & -2 & -1 & 3 \\ \( x_{i} \) & & & \\ \hline-2 & 0.1 & 0.15 & 0.2 \\ \hline-1 & 0.15 & 0.25 & 0.15 \\ \hline \end{tabular} Calculate the expected value and the dispersion of \( \tau \).