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for this question, i do not know how to find a linear transformation L

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Let X = [X1, X2] denote a Gaussian random vector with mean ux = [0, a] and covari-
ance Ex =
4 2
2
2
for some a E R
. Verify that Ex is a valid covariance matrix.
. What is the marginal pdf fx, (x1) for X1?
. Find the conditional density function fx,X2(X1/x2)
. Find a linear transformation L defining two new variables Y1, Y2 such that they are
uncorrelated to one another subject to the constraint that LL" = I:
[Y1, Y2] = L [X1, X2]
. Are Y1 and Y2 also statistically independent?

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