Define the N dimensional characteristic function for a random vector, X X1, X2, XN T , according to X () E ejTX where 1, 2, N T Show that the dimensional characteristic function for a zero mean Gaussian random vector is given by ga exp( cexg 0, ...

Define the N- dimensional characteristic function for a random vector, X = [X1, X2,..XN] T , according

Question:

Define the N- dimensional characteristic function for a random vector,
X = [X1, X2,€¦..XN] T , according to Î¦X (Î©) = E[ejÎ©TX] where
Î© = [Ï‰1, Ï‰2, Ï‰N] T. Show that the - dimensional characteristic function for a zero- mean Gaussian random vector is given by