15.5.18 Two-dimensional random variables and their characteristics

Problem: The random variable \( \xi \) is distributed according to Bernoulli's principle with the parameter \( p=0,65 \). Make the distribution table of the random vector \( \eta=\left(\xi_{1}, \xi_{2}\right)^{T} \), where \( \xi_{1}=\xi \), and \( \xi_{2}=\xi^{3} \). 1. Calculate the expected value of the random vector \( E[\eta] \) and its covariance matrix \( V_{\eta} \). 2. Find all conditional distribution series for the random variable \( \xi_{1} \) under the condition that the random variable \( \xi_{2}=y_{j} \).