The Largest Pool Size and Its Distribution
207
where a
T
p21
= (1, 1, . . . , 1) of dimension p – 1. Therefore,
( )
−
−
−
−
=
= =
−
+
∑
1
1
1
1
1
E
exp 2 ln
( )
p
T
p
j
p
p
p
j
Z X x
x c
m x
a
a
V
(C.17)
( )
(
)
−
−
−
−
=
−
−
−
= =
−
+
×
−
∑
1
1
1
1
1
1
1
1
Var
exp 2 ln
( )
exp
1
p
T
p
j
p
p
p
j
T
p
p
p
Z X x
x c
m x a
a
a
a
V
V
(C.18)
207
where a
T
p21
= (1, 1, . . . , 1) of dimension p – 1. Therefore,
( )
−
−
−
−
=
= =
−
+
∑
1
1
1
1
1
E
exp 2 ln
( )
p
T
p
j
p
p
p
j
Z X x
x c
m x
a
a
V
(C.17)
( )
(
)
−
−
−
−
=
−
−
−
= =
−
+
×
−
∑
1
1
1
1
1
1
1
1
Var
exp 2 ln
( )
exp
1
p
T
p
j
p
p
p
j
T
p
p
p
Z X x
x c
m x a
a
a
a
V
V
(C.18)