Question: Random vector. A random vector X with zero mean has a covariance matrix E)? with the following eigendecomposition 10 0 10010 0 1 1 1

Random vector. A random vector X with zero mean has a covariance matrix E)? with the following eigendecomposition 10 0 10010 0 1 1 1 1 Ejzo 00.50 055' (2) 0%% 000 o a. What is the variance of each of the entries of the random vector X1, X2 and X3? b. Is it possible to nd a unit-norm vector 11' such that the inner product between X and 11' (Le. the amplitude of the projection of X onto that direction) has variance greater than 1? c. Find three constants a1, a2 and (253, such that at least one of them is nonzero and P0112131 + :1ng + a3X3 = 0) = 1. Justify your answer mathematically, and interpret it geometrically

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