Let Y = (Yl, Y2, Y3)' have a N(J1" a2 J) distribution.

Consider the quadratic forms defined by the matrices Ml , M2 , and M3 given below.

(a) Find the distribution of each Y'MiY.

(b) Show that the quadratic forms are pairwise independent.

(c) Show that the quadratic forms are mutually independent.

M2 = 114 [ -3 1 2, 9 -3 -6]

-6 2 4 M3 = ~ [ -5 25 - 20 . 1 -5 4]

42 4 -20 16