Suppose Microeconomic Principles and Macroeconomic Principles both have two recommended textbooks. The bivariate distribution of the number of micro and macro textbooks actually purchased by economics students is

Micro, X Macro, Y X=0, X=1, X=2, Y=0 0.15 0.15 0.05 Y=1 0.15 0.10 0.05 Y=2 0 0.05 0.30 1

(a) Find the marginal distributions for the number of micro and macro textbooks purchased by each student.

(b) Compute E(X), E(Y), Var(X), Var(Y), Cov(X,Y), and Corr(X,Y) (c) Compute Var(X+Y)

(d) Are the number of micro books purchased an the number of macro books purchased by each student independent?

(e) Write down the probability distribution of X conditional on Y= 0, i.e. the distribution of micro textbooks purchased by a student who has purchased zero macro textbooks.

(f) Compute E(XjY=0) and Var(XjY=0)