Suppose a student is randomly selected from your school. Which of the following pairs of random variables are most likely independent?

(a)$X=$student’s height; $Y$= student’s weight

(b) $X$= student’s IQ;$Y$ = student’s GPA

(c) $X$= student’s PSAT Math score;$Y$ = student’s PSAT Verbal score

(d)$X$= average amount of homework the student does per night;$Y$ = student’s GPA

(e)$X$ = average amount of homework the student does per night; $Y$ = student’s height

Given in the question that, Suppose a student is randomly selected from your school . We need find the independent pairs of random variables from the options.

If a difference in one variable has no effect on the other, the assumption of independence can be made.

1. Not self-sufficient, because the taller a pupil is, the heavier he or she tends to be.
2. No, because a higher IQ has a direct effect on GPA, i.e. the GPA will be higher as well.
3. Not independent, because if your math score is greater, your verbal score will be higher as well.
4. Not independent, because if more homework is completed, the GPA is predicted to rise as well.
5. Unaffected by the amount of homework completed, because the student's height is unaffected by the amount of schoolwork completed.