The task: Find out expected value of $\xi^2\eta^2$, where $(\xi,\eta)$ has normal distribution with zero mean vector and covariance matrix $(\begin{matrix} 4 & 1 \\ 1 & 1 \\ \end{matrix})$
I tryed to find the expected value with new random value as ($\eta- c\xi$), where c=const and cov($\xi, \eta- c\xi$)=0, but it only complicates the calculations.