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###### Random vector. random vector X with zero mean has a covariance matrix Zx with the following eigendecomposition Zx {416 0.5 (2) 0 } What is the variance of each of the entries of the random vector X1, Xz and X3? b. Is it possible to find a unit-norm vector U such that the inner product between X and & (i.e. the amplitude of the projection of X onto that direction) has variance greater than 1? Find three constants 01, 42 and 43, such that at least one of them is nonzero and P(a1X} + (2Xz + a3

Random vector. random vector X with zero mean has a covariance matrix Zx with the following eigendecomposition Zx {416 0.5 (2) 0 } What is the variance of each of the entries of the random vector X1, Xz and X3? b. Is it possible to find a unit-norm vector U such that the inner product between X and & (i.e. the amplitude of the projection of X onto that direction) has variance greater than 1? Find three constants 01, 42 and 43, such that at least one of them is nonzero and P(a1X} + (2Xz + a3X3 = 0) = 1. Justify your answer mathematically; and interpret it geometrically:

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