Question: the question as screenshots Random vector. A random vector X with zero mean has a covariance matrix _ with the following eigendecomposition 0 O (2)

the question as screenshots

Random vector. A random vector X with zero mean has a covariance matrix _ with the following eigendecomposition 0 O (2) a. What is the variance of each of the entries of the random vector X1, X2 and X3? b. Is it possible to find a unit-norm vector u such that the projection of X onto u has variance greater than 1? c. Find three constants a], a2 and as, such that at least one of them is nonzero and P(a X, + a2X2 + (3X3 =0) = 1. Justify your answer mathematically, and interpret it geometrically

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