Show that the two random variables of Exercise 102 are not independent.
Exercise 102
A certain college gives aptitude tests in the sciences and the humanities to all entering freshmen. If X and Y are, respectively, the proportions of correct answers that a student gets on the tests in the two subjects, the joint probability distribution of these random variables can be approximated with the joint probability density
What are the probabilities that a student will get
(a) less than 0.40 on both tests;
(b) more than 0.80 on the science test and less than 0.50 on the humanities test?