15.2.23 One dimensional random variables and their characteristics

Problem: There is a safe in the depository of the bank, where \( 80.000 \$ \) are kept. During the day, some amount of money (random variable \( \xi \) ), not known in advance, can be demanded from the safe. The distribution table of the random variable \( \xi \) has the following form: \begin{tabular}{|c|c|c|c|c|c|} \hline\( x_{i} \) & \( 10000 \$ \) & \( 15000 \$ \) & \( 20000 \$ \) & \( 25000 \$ \) & \( 30000 \$ \) \\ \hline\( p_{i} \) & 0.2 & 0.15 & 0.25 & 0.19 & 0.21 \\ \hline \end{tabular} 1. Make the distribution table of the random variable \( \tau \)-the amount of money, remaining in the safe, if \( \tau=80000-\xi \). 2. Find the distribution function of this random variable \( \tau \). 3. Calculate the expected value and the dispersion \( E[\tau], V[\tau] \).