The question looks like this, where fx is equal to this:
$f(x) = exp(-(1/2(1 - \rho^2 - \gamma^2))(1-\gamma^2)x_1^2 + x_2^2 + (1-\rho^2)x_3^2 -2\rho x_1 x_2 +2 \rho \gamma x_1 x_3 -2 \gamma x_2 x_3))/(2\pi)^3/2(\sqrt(1-\rho^2 - \gamma^2)$
I need to find the probability density function of $X_1$ alone and $X_2 + X_3$ together. I know how to find probability density function of $X_1$ alone which is integrating the above expression wrt to $X_2, X_3$. But not sure how to find probability density function of $X_2 + X_3$.
Moreover, I need to find joint density function of $X_1$ and $X_2 + X_3$. I am not sure how to do this as well.
Is there any way of finding the density function without integrating wrt to $X_1$ or $X_2 + X_3$?
Need some guidance on solving this.