Q2 Z2,(Q2) Z2(Q2) - Institute for Water Resources - U.S. Army

Let us define n(X 1 ) as the probability distribution of
i
Xiji over the ith population. Then, say, n 1 (X21 ) is the probability
distribution of X 21 over the barge origin population. The n.(X )
ij
are assumed to be normally distributed with means p ij and
variances ja i. It follows that
(8 )
(9)
1
1 . (20 -2 . e
n (X ) a
„Lid_ .
iJ
1 . (20 . e
n i (Xi .) 4 0. 4 . (X - U. ) 2
ln 7,7 7 71:7 = in till in
3 13 i
ij 2 " 2 1 li
a
J 11
'
(X. - • ) 2
11 1 ii
2 2 i
a
ij
( 10) = ln + ( ia li
)A + 2 X. ( U 0 2 U 2 )
11 i eii
. ia ij 2 2
2
or
U 2
a 2
U
2 2
j i
2 2
2
i
a
ij j
a
ij
n (X..)
(11) in
n X
- a. + b. X + c X 2
. ) lj ij ij ij
.U2 .a. ? U 0 2
i 2 2
ii 2 a
iij i ij
ki
where a = in 2.4-1 + 111L11 .
(12)
2 2 2
bij = j aij - j Uij laijViaij f.
cij = 1 02ii 72 1.02ij
Pii) 2/2 gij
'4)(14 2412 jail
17