... (2ncf;)- 2 exp{-(x2-P2 )2/ 2~~ ,2) (2. 56) and f(xJx2;)= [27 ro:(1-p2)]- 2 Xexp{-[x,-~,-p, .2( x2- ~2) 12/ 2(1-p2)o:}, (2. 57) where p, = a,p/u, From (2. 56), it is seen that the marginal pdf for Z2 is normal ... (2~ )-“ 21 G,111~2exp{- (2. 67a) and dx,lce,) = w- m2’ - %GII’ 21 G 22 G 121 1/2w{- Q2 /2) , (2. 67b) with mi the number of elements in xi, i = 1 ,2, ml + m2 = m, Q,, and Q2 as defined in (2. 65) and (2. 66), ... conditional variance - p2 Since t, = (2, - p2)/u2 the conditional pdf for Z2, given Z,, is normal, that is, f(x,lx,J)= [2nu;(1-PZ)]- 2 Xexp{-[x2- ~2 - _2 .~(x~-11.~) 12/ 2(1-P2)u 22} ~ u2), wheree’ (P,P,,...