Question: Show that the two random variables of Exercise 3.102 are not independent. In exercise A certain college gives aptitude tests in the sciences and the

Show that the two random variables of Exercise 3.102 are not independent.

In exercise

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

(23y for 0

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