Solving this question will (hopefully) also solve the confusion I have in my previous question.
I have two random Gaussian variables $A$ and $B$ with $\mu_A, \mu_B$ and $\sigma_A, \sigma_B$ respectively.
I have the constraint that $Z=AB^3$ is Gaussian with $\mu_Z$ and $\sigma_Z$. How can I determine the $\text{Cov}\left(A,B\right)$?
My end goal is to run a simulation that uses these variables that satisfy the constraint above. I think that I need to know the covariance between $A$ and $B$ in order to correctly generate them and satisfy all the above conditions.
Does anybody have any suggestions on how to move forward?