Zero Covariance Trap

Let XX be uniform on {−1,0,1}{-1, 0, 1} and let Y=X2Y = X^2. Which statement correctly describes the relationship between XX and YY?

A

X and Y are both uncorrelated and independent

B

Cov(X,Y) is undefined since Y is deterministic given X

C

X and Y are uncorrelated but not independent

D

X and Y are independent

E

X and Y are correlated and dependent