If X,YX,YX,Y independent with E[X]=1,Var(X)=1E[X]=1, Var(X)=1E[X]=1,Var(X)=1, and Y=X2Y=X^2Y=X2, are they independent?
Yes, always
No, never
Yes, because E[XY]=E[X]E[Y]E[XY]=E[X]E[Y]E[XY]=E[X]E[Y]
Cannot determine