Q. 1. Suppose at Columbia University, grade point average (GPA) and SAT scores are related by the conditional expectation E(GPA|SAT) = .90 + .001 SAT.
a. Find the expected GPA when SAT = 1600.
b. Find E(GPA|SAT=2200)
c. If the average SAT in the university is 2000, what is the average GPA?
2. Let u and X be two random variables that satisfy E [u|X] = 0 and E[u^2 |X]= o-^2.
a. Find the unconditional mean and variance of u.
b. What is the covariance between u and X?