# Question: Define the N dimensional characteristic function for a random vector X

Define the N- dimensional characteristic function for a random vector,

X = [X1, X2,…..XN] T , according to ΦX (Ω) = E[ejΩTX] where

Ω = [ω1, ω2, ωN] T. Show that the - dimensional characteristic function for a zero- mean Gaussian random vector is given by

X = [X1, X2,…..XN] T , according to ΦX (Ω) = E[ejΩTX] where

Ω = [ω1, ω2, ωN] T. Show that the - dimensional characteristic function for a zero- mean Gaussian random vector is given by

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