Question: Let ( x , Y ) be a centered Gaussian vector with E ( x 2 ) = 4 and E ( Y 2 )

Let (x,Y) be a centered Gaussian vector with E(x2)=4 and E(Y2)=1, and
such that the variables 2x+Y and x-3Y are independent.
Determine the covariance matrix of (x,Y).
Show that the vector (x+Y,2x-Y) is also Gaussian, then determine its
covariance matrix.
Calculate E(|x+Y,2x-Y|).
Let (x,Y) be a centered Gaussian vector with E(x2)=4 and E(Y2)=1,

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