Let X and Y be i.i.d. N(0, 1), and let S be a random sign (1 or -1, with equal probabilities) independent of (X, Y).
(a) Determine whether or not (X, Y,X + Y) is Multivariate Normal.
(b) Determine whether or not (X, Y, SX + SY) is Multivariate Normal.
(c) Determine whether or not (SX, SY) is Multivariate Normal.
I have gotten to the matrix part but not sure how to show if they are multivariate or not. Here is where I am up to.
