15.2.11 One dimensional random variables and their characteristics

Problem: The distribution table of the discrete random variable \( \xi \) has the form: \begin{tabular}{|c|c|c|c|c|c|} \hline\( x_{\mathrm{i}} \) & -2 & -1 & 0 & 1 & 2 \\ \hline\( p_{i} \) & 0.2 & 0.2 & 0.2 & 0.2 & 0.2 \\ \hline \end{tabular} Make distribution tables for random variables \( \tau_{i}, i=1,2,3 \) if: \( \tau_{1}=-\xi, \tau_{2}=|\xi|, \tau_{3}=\xi^{2} \). Determine the expected values \( E\left[\tau_{i}\right] \) and the dispersions \( V\left[\tau_{i}\right], i=1,2,3 \).