SupposeXandYare continuous random variables with joint pdffX,Y(x, y).

1. IfCov(X, Y) = 0, can we claim thatXandYare independent? If yes, supply a proof. If no, provide a conter-example.
2. If (X,Y)N2(0,0,1,1,), andCov(X,Y) = 0. Can we claim thatXandYare independent? If yes, supply a proof. If no, provide a conter-example.
3. If (X,Y)N2(0,0,1,1,), andCov(X,Y) = 0, defineC=Y/X. Find the pdf ofC (show your work)