A study of bicycle riders found that a male cyclist's speed X (in miles per hour over a 100 mile 'century" ride) and weight 1' (kg) could be modeled by a bivariate Gaussian PDF fx,y(x, y) with parameters μx = 20, σx = 2, ,μy = 75, σy = 5 and pX,Y = -0.6. In addition, a female cyclist's speed X' and weight Y' could he modeled by a bivariate Gaussian PDF fX',Y'(x', y') with parameters μx' = 15, σx' = 2, μy = 50, U)' = 5 and PX',Y' = -0.6. For men and women, the negative correlation of speed and weight reflects the common wisdom that fast cyclists are thin. As it happens, cycling is much more popular among men than women; in a mixed group of cyclists, a cyclist is a male with probability p = 0.80.

You suspect it's OK to ignore the differences between man and women since for both groups, weight and speed are negatively correlated, with p = -0.6. To convince yourself this is OK, you decide to study the speed X^ and weight Y^ of a cyclist randomly chosen from a large mixed group of male and female cyclists. How are X^ and Y^ correlated? Explain your answer.