Two continuous random variables X and Y have a joint probability distribution
f ( x, y ) = A ( x 2 + y 2 ) ,
where A is a constant and 0 ≤ x ≤ a ,0 ≤ y ≤ a . Show that X and Y are negatively correlated with correlation coefficient -15 / 73. By sketching a rough contour map of f ( x, y ) and marking off the regions of positive and negative correlation, convince yourself that this (perhaps counter-intuitive) result is plausible.