Question: Given a Gaussian random vector x N ( , ) where = [ 0 1 0 ] T and = [ 1 0 1 0

Given a Gaussian random vector xN(,) where =[010]T and =[101090104].
a. What is the pdf of Z=x1+x3.
b. What is the probability P(Z0) in terms of Q-functions.
c. Find the MMSE estimate of x3 given (x1,x2).
d. What is the joint pdf of Y=Ax+b, where A=[2010-10] and b=[-3-1]T.
Given a Gaussian random vector xN(,) where =[010]T and =[101090104]. a.

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