8.2 Consider three universities: Harvard, Columbia, and NYU. Harvard and Columbia are in the Ivy League, but NYU is not. Columbia and NYU are in New York City, but Harvard is not. You have a large population of students, of whom one-third attend each school. You pick two students from this population at random. X is a random variable that equals the number of students chosen who go to school in New York City. Y is a random variable that equals the number of students chosen who attend an Ivy League institution. (a) Find p(X, Y). (b) Are X and Y independent? Fully justify your answer. (c) Provide a verbal explanation of your answer to part (b). 8.3 8.3) Redo problem 8.2 presuming that in your population of stu- dents 50% attend NYU, 20% attend Harvard, and 30% attend Columbia.