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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?

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