Question: Let Var[y] = I and z 1 = Ay and z 2 = By be linear transformations of y. (a) Show that Var[z 1 ]

Let Var[y] = I and z1 = Ay and z2 = By be linear transformations of y.

(a) Show that Var[z1] = AA' and Cov[z1, z2] = AB'.

(b) Why, for general A, are the elements of z1 correlated although the elements of y are not?

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