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2) Assume that the random vector X = (X, Y) has covariance matrix COV[X]. Assume E[X] = E[Y] = 0. a) Why do the eigenvectors

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2) Assume that the random vector X = (X, Y) has covariance matrix COV[X]. Assume E[X] = E[Y] = 0. a) Why do the eigenvectors of COV[X] represent the direction of maximum, resp. minimum fluctuation? b) Why are the eigenvectors orthogonal to each other

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