Average and standard deviation of linear combination. Let r1,.., be n-vectors, and a1...., ak be mumbers, and consider the linear combination z = a11 + ..+akak. (a) Show that avg(z) = a1 avg(21)+ + ar avg(Tk). (b) Now suppose the vectors are uncorrelated, which means that for i # j, r and r, are uncorrelated. Show that std(z) = Vaf std(r1) + ...+af std(rk)2.