(b) (10 points) [Covariance Matrix] The variance–covariance matrix or simply the covariance matrix, which will be used later in this course, can be regarded as a generalization from a measure of the variation of a single random variable X to a vector of random variables X = [X1, . . . , Xn] T . Its mathematical definition is as follows Cov(X) = E (X ? E[X])(X ? E[X])T (4) and your job is to verify using simple matrix operations that the covariance matrix is a square matrix consisting of variance terms on the diagonal and covariance terms off the diagonal. Prove that the elementwise expression of the covariance matrix for a length-3 random vector X = [X1, X2, X3] T is as follows: Cov(X) = ? ? ? Var(X1) Cov(X1, X2) Cov(X1, X3) Cov(X2, X1) Var(X2) Cov(X2, X3) Cov(X3, X1) Cov(X3, X2) Var(X3) ? ? ? . (5) Hint: Write variance and covariance in terms of E[·] will be helpful. This problem has practical uses in linear/quadratic discriminant analysis.