I have the following density function which is a mixture of bivariate Gaussian distributions -
\begin{equation*} f(\mathbf{x})=\frac{1}{3}\mathbf{N}_2(\mathbf{0},\mathbf{I}_2)+\frac{1}{3}\mathbf{N}_2\biggl\{\left(\begin{array}{c}-6 \\-6\end{array}\right),\left(\begin{array}{cc}1 & 0.9 \\0.9 & 1\end{array}\right)\biggr\}+\frac{1}{3}\mathbf{N}_2\biggl\{\left(\begin{array}{c}4 \\4\end{array}\right),\left(\begin{array}{cc} 1 & -0.9 \\-0.9 & 1\end{array}\right)\biggr\} \end{equation*}
My question is - how do I assess whether or not the parameters are correlated by examining the covariance matrices?
Thank you for your help!