A random point in space is given by three rectangular coordinates forming a system of normal random variables with the probability density f(x, y, z) = 3 16773/2 exp { - 1112x² [2x² + 4y² − 2y(z + 5) + (z 5)²]}. (a) Find the covariance matrix, (b) determine the locus of points when the probability is 0.01.

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