How to use collect() or coeffs() on random variables instead of standard variables?
I need to re-organize a linear combination of RVs nu, nu, u, u, u by collecting the coefficients on each of these 5 RVs. Note that the Xs are correlated with each other and the Ys are correlated with each other (but Xs and Ys are uncorrelated).
For example, nu is a 2D gaussian vector where nu and nu are defined in terms of _R1, _R2, means, standard deviations and correlation coefficient. They are quite "nested" and the 3D gaussian vector u is even worse, so when these enter a linear combination it becomes hard to identify them back as simply nu, nu, u, u, u.
Is there a way to "isolate" them in a linear combination by using collect()-like or coeffs()-like functions (i) directly on the RVs or (ii) indireclty on the explicit expressions of _Rs, means, standard devs, correlation coeffs?
(I already checked the answers to these two somewhat similar questions but did not help for my case:
See my script below:
For example, I would want collect() on nu (or equivalently on _R1*sigma__v+nu__0) to give me X__1+X__3 (as you easily see from my definition of Omega).