An experiment produces a zero mean Gaussian random vector X = [X1 ··· Xk] with correlation matrix R = E[XX']. To estimate R, we perform n independent trials, yielding the iid sample vectors X(1), X(2), . . . , X(n), and form the sample correlation matrix
(a) Show 
(n) is unbiased by showing E[ (n)] = R.
(b) Show that the sequence of estimates (n)is consistent by showing that every element ij(n) of the matrix converges to Rij . That is, show that for any c > 0,
