Data from 2013 posted on the Williams College website shows that of all 3,195 males applying, 18.2% were admitted, and of all 3,658 females applying, 16.9% were admitted. Let X denote gender of applicant and Y denote whether admitted.
a. Which conditional distributions do these percentages refer to, those of Y at given categories of X, or those of X at given categories of Y? Set up a table showing the two conditional distributions.
b. Are X and Y independent or dependent? Explain.