15.2.52 One dimensional random variables and their characteristics

Problem: Let the random variables \( X \) and \( Y \) be independent and given in accordance with the laws of distribution: \begin{tabular}{|c|c|c|c|} \hline\( x_{i} \) & 2 & 3 & 4 \\ \hline\( p_{i} \) & 0,3 & 0,2 & 0,5 \\ \hline \end{tabular} \begin{tabular}{|c|c|c|c|c|} \hline\( y_{i} \) & 0 & 1 & 2 & 3 \\ \hline\( q_{i} \) & 0,2 & 0,4 & 0,1 & 0,3 \\ \hline \end{tabular} Find the distribution law of the variable \( Z=X-Y \) and the expected value and dispersion of the variables \( X, Y \) and \( Z \).