Let, for k 1, k = E(X-EX)k be the kth central moment of the random variable X. Prove that the matrix 10/2 0 12 13 12 13 14 (a) has a non-negative determinant; (b) is non-negative definite. Assume w.l.o.g. that E X = 0 and investigate E (ao + aX + aX), where ao, 91, 92 R. (c) Generalize to higher dimensions. Solve a,b,c in details