Consider the sample covariance matrix Sn defined by (16.4), where X1, . . . , Xn are independent ∼ N(μ, Ip) and μ is a p-dimensional mean vector. Show that, when p is fixed, we have Sn

−→P Ip and

√

n(Sn −Ip)

−→d Wp, where Wp is a Wigner matrix [defined below (16.9)], whose upper off-diagonal entries are N(0, 1) and diagonal entries are N(0, 2).