Question: 1. Jointly Gaussian [10 points, 5 points, 5 points] Consider a 3-dimensional Gaussian random vector (X1, X2, X3) with zero mean and covariance matrix given

1. Jointly Gaussian [10 points, 5 points, 5 points] Consider a
3-dimensional Gaussian random vector (X1, X2, X3) with zero mean and covariance

1. Jointly Gaussian [10 points, 5 points, 5 points] Consider a 3-dimensional Gaussian random vector (X1, X2, X3) with zero mean and covariance matrix given by 5 2 2 2 5 2 2 2 (a) Find E[X1|X2, X3] directly from fx, X2,X3(21|202, 203). (b) Show that the LMMSE of X1 from X2 and X3 is equal to E[X1|X2, X3]. (c) Using part (b), and the fact that Var(X1|X2, X3) is equal to the minimum mean square error, find Var(X1|X2, X3)

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