Question: Random vector. A random vector X with zero mean has a covariance matrix 2)? with the following eigendecomposition l 0 0 1 0 0 1

Random vector. A random vector X with zero mean has a covariance matrix 2)? with the following eigendecomposition l 0 0 1 0 0 1 0 0 1 1 1 1 EX: 0 E E 0 0.5 0 0 V E . (2) 0 i % 0 O 0 0 % 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 21' 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 (13, such that at least one of them is nonzero and P(a1X1 + 0,ng + a3X3 = 0) = 1. Justify your answer mathematically, and interpret it geometrically

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