Let Y = (YI, Y2, Y3)' be a random vector. Suppose that E(Y) EM, where M is defined by M = {

(a, a -

b, 2b),la, bE R}.

(a) Show that M is a vector space.

(b) Find a basis for M.

(c) Write a linear model for this problem (i.e., find X such that Y =

X/3 +

e, E

(e) = 0).

(d) If /3 = (/31,/32)' in part (c), find two vectors r = (rI,r2,r3)' and s = (Sl,S2,S3)' such that E(r'Y) = r'X/3 = /31 and E(s'Y) = /32.

Find another vector t = (t1, t2, t3)' with r ¥- t but E(t'Y) = /31.