(a) Let X1, X2 be indep N(u, 62). What is the distribution of 1+42? (X1 -X21 ' (b) Let Z1, Z2, Z3 be iid N(0, 1) random variables. There is a constant c and a degrees of freedom r such that W =c (Z1 -Z2)2 + (Z2-Z3)2+ (Z3-Zi)2|has a x, distribution. Find c and r, and show that W~ X-. [ It might help to write W as Z'AZ for some 3 x 3 matrix A. ]