# 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

## Relevant Questions

For any four zero- mean Gaussian random variables X1, X2, X3, and X4, show that . E [X1X2X3X4] = E [X1X2] E[X3X4] + E [X1X3] E [X2X4] + E [X1X4] E [X2X3] You might want to use the result of the previous exercise. Note: This ...Show that the derivative of reduces to the form Repeat exercise 6.28 Assuming we wish to find an estimate of V given the observation U = u. (a) Find the MAP estimator of U given the observation V = v. (b) Find the ML estimator of U given the observation V= v. (c) Find ...The traffic managers of toll roads and toll bridges need specific information to properly staff the toll booths so that the queues are minimized (i. e., the waiting time is minimized). (a) Assume that there is one toll ...Suppose N1is a discrete random variable equally likely to take on any integer in the set {1, 2, 3}. Given that, N1 = n1, the random variable N2 is equally likely to take on any integer in the set {1, 2… n2}. Finally, given ...Post your question