Solution
= Solution
Completing the square gives $X,Y\sim N(0,4/3)$, so each marginal is $\sqrt3(2\sqrt{2\pi})^{-1}e^{-3x^2/8}$. Their covariance is $2/3$, so they are not independent.
= Solution
Completing the square gives $X,Y\sim N(0,4/3)$, so each marginal is $\sqrt3(2\sqrt{2\pi})^{-1}e^{-3x^2/8}$. Their covariance is $2/3$, so they are not independent.