T he 2 x 2 inatrix [ cos e Q = sine - sin el cos e is
Chapter 8, Problem 8.47(choose chapter or problem)
T he 2 x 2 inatrix [ cos e Q = sine - sin el cos e is called a rotation matrix because y = Qx is the rotation of x by the angle e. Suppose X = [X1 X2] ' is a Gaussian (0, C x ) vector where Cx = diag[a f, a~] and a~ > a i . Let Y = QX. (a) Find the covariance of Y1 and Y2. Show that Y1 and Y2 are independent for all e "f 2 2 1 0"1 = 0"2 . (b) Suppose a~ > af. For what values e are Y1 and Y2 independent?
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