15.5.3 Two-dimensional random variables and their characteristics

Problem: A two-dimensional random variable \( (\xi, \eta) \) is uniformly distributed in the triangle \( A B C \) with the vertices \( A(-1,0), B(0,2), C(0,-2) \). Find the distribution function of the probability \( (\xi, \eta) \), the marginal densities of the distribution \( \xi, \eta \), the expected values, dispersions, covariance and the correlation coefficient. Are the variables \( \xi, \eta \) independent?