A particle impinges randomly and uniformly on a square detector with vertices at (Carte- sian) coordinates, (1,0), (0, 1), (2,1) and (1,2) (arbitrary units). Let the coordinates of the particle be (X,Y). (i) Plot the marginal distributions of X and Y, respectively, and evaluate the. correla- tion coefficient, pxY. Hence, argue that the coordinates are uncorrelated but not independent. (ii) Plot the regression function of Y, given X = , including the standard interval in your plot.