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3. (a) Partition the random vector X, and its covariance matrix E, as follows: X = X1 Ell E12 X 2 E = E21 _22 Assuming Ezz is non-singular, define Y = X1 - E12Ez X2 Y2 X 2 Write Y in the form CX and define C. What is the determinant of C? What is the covariance of Y, and Yz?(b) X = (X1, X2, X3)' follows a multivariate normal distribution with mean H = (#1, #2, /3)' and covariance matrix Cov (X ) = ) = p 0 show that the conditional distribution of (X1, X2) given X; has mean vector [1 + p'(13 - 13), #2]' and covariance matrix