Solution
= Solution
\b[Zero correlation means that the variables are uncorrelated:] $E[(X-EX)(Y-EY)]=0$, or equivalently $E(XY)=EX\,EY$. It does not imply <independence>. For example, if $X$ is uniform on $[-1,1]$ and $Y=X^2$, symmetry gives $EX=E(X^3)=0$, hence zero <covariance>, although $Y$ is determined by $X$. Both <random variables> are non-constant and have finite positive <variances>.