15.5.6 Two-dimensional random variables and their characteristics

Problem: The ball is tossed into the basketball hoop. The probability of a success by one toss is equal to 0,7 . Let the random variable \( \xi_{1} \) be the number of successful tosses, and the random variable \( \xi_{2} \) be the number of misses by one toss. 1. Make a table of the joint distribution of these random variables. 2. Calculate the expected values of these random variables and write down the expected value of the vector \( \eta=\left(\xi_{1}, \xi_{2}\right)^{T} \). 3. Calculate the dispersions, the correlation moment and the correlation coefficient of these random variables. Write the covariance and correlation matrices. 4. Will these random variables be connected to each other linearly?