4. Let x = (21, ...,"p)' be a random vector with multivariate normal distribution N(u, E). Partition a into two sub-vectors x] and x2, and partition the mean vector and covariance matrix accordingly as C1 E = Ell E12 H = E21 222 (a) Define z2 = $2 - [/2 + E21 En (x1 - #1)] . Show that Ez2 = 0. (b) Show that Cov($1, 22) = 0 and Var(z2) = E22 - E21 En E12. (c) Conclude from part (a) and (b) that Var($2 x]) = [22 - E21 En E12