b
t
t
v
t
t
z
t
=b
t
v
t
:
Z=b
T(x)
v
T(x)
:
n
n
n
8
<
:
1; t¬n
b
t
=
0; t>n
v
t
= v
t
;
t0;
8
<
:
v
T(x)
; T(x)¬n
Z =
0;
T(x)>n
E[Z]
n
A
1
x:nj
Z
Z
1
0
z
t
g(t)dt=
n
0
v
t
t
p
x
x+t
dt:
A
1
x:
nj
=E[Z]=
j
Z
Z
h
Z
j
i
n
j
v
t
E
=
t
p
x
x+t
dt
0
Z
n
0
e
(j)t
t
p
x
x+t
dt:
=
j
Z
n
(j)
x
t
t
b
t
v
t
b
j
t
=b
t
t E[Z
j
]
t
E[Z]
(j
t
) j>0
E[Z
j
]@
t
=E[Z]@(j
t
)
h
i
h
i
Z
j
(b
T(x)
v
T(x)
)
j
E
= E
h
i
b
j
T(x)
v
j
T(x)
= E
h
i
b
T(x)
v
j
T(x)
= E
:
Z
t
0
s
ds
v
t
=exp
;
t
j
Z
t
0
j
s
ds
v
j
t
=exp
;
(j
t
)
A
1
2
Var[Z]=
2
A
1
x:nj
;
x:nj
2
A
1
n
x:nj
2
b
t
= 1;
t0;
v
t
= v
t
;
t0;
Z = v
T(x)
;
T(x)0:
Z
1
0
v
t
t
p
x
x+t
dt:
A
x
=E[Z]=
A
x
2
Var[Z]=
2
A
x
;
2
A
x
2
2
30:05:98
!=100
(40)
100
a
60j
=20
A
40
a
60j
=10;6
A
40
Z
s(40)
s
0
(40+t)
60
0
100v
t
s(40+t)
(A
40
)
j100
=
s(40+t)
dt
Z
s(x)=1
x
100
=
100
60
60
0
v
t
dt
=
=
100
60
a
60j
=
100
60
20=
100
3
;
Z
s(40)
s
0
(40+t)
0
(100)
2
v
2t
s(40+t)
60
(
2
A
40
)
j100
=
s(40+t)
dt
Z
s(x)=1
x
100
=
10:000
60
60
0
v
2t
dt
=
=
10:000
60
a
60j
0
=2
=
10:000
60
10;6
2
Var(Z)=
10:000
100
3
60
10;6
655;(5);
660
n
n
n
n
n
8
<
:
0; t¬n
b
t
=
1; t>n
v
t
= v
n
;
t0;
8
<
:
0; T(x)¬n
Z =
v
n
; T(x)>n
A
1
x:nj
=E[Z]=v
n
P(T(x)>n)=v
n
n
p
x
E[Z
2
]=v
2n
P(T(x)>n)=v
2n
n
p
x
:
Var[Z] = v
2n
n
p
x
(v
n
n
p
x
)
2
=v
2n
n
p
x
n
q
x
2
=
2
A
1
A
1
x:nj
:
x:nj
n
n
n
n
n
b
t
= 1;
t0;
8
<
:
v
t
;
t¬n
v
t
=
v
n
; t>n
8
<
:
v
T(x)
; T(x)¬n
Z =
v
n
;
T(x)>n
A
x:nj
Z
1
Z
2
Z
3
n
n
n
8
<
:
v
T(x)
; T(x)¬n
Z
1
=
0;
T(x)>n
8
<
:
0; T(x)¬n
Z
2
=
v
n
; T(x)>n
8
<
:
v
T(x)
; T(x)¬n
Z
3
=
v
n
;
T(x)>n
Z
3
=Z
1
+Z
2