Question: Please see the problem in the attachment. Consider a 3-dimensional Gaussian random vector (Xl , X2, X3) with zero mean and covariance matrix given by

Consider a 3-dimensional Gaussian random vector (Xl , X2, X3) with zero

Please see the problem in the attachment.

Consider a 3-dimensional Gaussian random vector (Xl , X2, X3) with zero mean and covariance matrix given by 522 252 225 (a) Find directly from x3). (b) Show that the LMNISE of from and X3 is equal to X3]. (c) Using part (b), and the fact that Var(X1 IX2, X3) is equal to the minimum mean square error, find Var(X1 IX2, X3).

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