3. (Random vector) A random vector a with zero mean has a covariance matrix Er with the following eigendecomposition O O O O E= = O 0 (1) (a) What is the variance of each of the entries of the random vector *[1], *[2] and *[3]? (b) Is it possible to find a unit-norm vector u such that the inner product between a and u (i.e. the amplitude of the projection of a onto that direction) has variance greater than 1? (c) Find three constants a1, a2 and a3, such that at least one of them is nonzero and P(aix[1]+a2x[2]+a3x [3] =0) = 1. Justify your answer mathematically, and interpret it geometrically