8
<
:
P(K(x)¬m(x))
1
2
;
P(K(x)m(x))
1
2
:
3:13
1600
10
10
540
x l
x
0 40
10 39
70 26
Y
1
Y
2
70
c
P(Y
1
+Y
2
>c)=0;05:
T
i
(x)
l
t
10
=s(10)l
t
0
=s(10)40)s(10)=
39
40
:
l
2
10
=s(10)l
2
0
)l
2
0
=
54040
554:
39
l
2
0
= 554
l
1
0
= 1600
l
0
= 2154
Y
1
+Y
2
70
Y =Y
1
+Y
2
(l
0
;s(70))
s(70) =
l
t
70
=
1
20
EY]= l
0
s(70) =
1
20
2154
VarY]=
l
t
0
l
0
s(70)(1s(70))=
1
20
20
2154
0
@
(Y
1
+Y
2
)E(Y
1
+Y
2
)
1
A
>
c
1
20
2154
P(Y
1
+Y
2
>c)=P
=0;05:
q
q
13
20
20
2154
Var(Y
1
+Y
2
)
0
@
c
1
20
2154
1
A
1
=0;95
q
13
20
20
2154
c
1
20
2154
1;645)c1436;4136:
q
13
20
20
2154
T(x)
s(x)
x2f0;1;:::g;0¬t¬1
s(x+t)=(1t)s(x)+ts(x+1)
s(x+t)=s(x)e
x
t
x
=np
x
s(x+t)
=
1t
1
s(x)
+
t
s(x+1)
1e
x
t
tq
x
1(1t)q
x
t
q
x
tq
x
p
x
1(1t)q
x
e
x
t
t
p
x
1tq
x
yq
x
1tq
x
yq
x
1(1yt)q
x
1e
x
y
y
q
x+t
q
x
1tq
x
q
x
1(1t)q
x
x+t
x
p
x
q
x
[1(1t)q
x
]
2
e
x
t
x
t
p
x
x+t
q
x
0<t<1 0¬y ¬1 y+t¬1
t=0 t=1
t
q
x
=1
s(x+t)
j=1
(1t)s(x)+ts(x+1)
s(x)
=j
s(x)
=1(1t)t
s(x+1)
s(x)
=tt
s(x+1)
1
s(x+1)
s(x)
s(x)
=t
=tq
x
y
q
x+t
=1
s(x+t+y)
j=1
(1ty)s(x)+(t+y)s(x+1)
(1t)s(x)+ts(x+1)
s(x+t)
=j
s(x)t[s(x)s(x+1)]
=
y
[
1
s(x+1)
s(x)
]
1t
[
1
s(x+1)
=
ys(x)ys(x+1)
s(x)
]
=
yq
x
1tq
x
(1t)s(x)+ts(x+1)
=
1
s(x+1)
x+t
=
s
0
(x+t)
s(x)s(x+1)
s(x+t)
=j
j=
s(x)
1t
(
1
s(x+1)
s(x)
)
=
q
x
1tq
x
3:24
3:2
55
T(x) x=0
T(0)
P(T(0)>m(0))=
1
2
s(m(0))=
l
m(0)
l
0
=
1
2
:
3:2
l
77
=51599 l
78
=48878
(77;78)
s(77+t)=(1t)s(77)+ts(78)=0;5
(1t)l
77
+tl
78
=50000:
t=0;5876516:
m(0)=77;5876516:
T(x)=K(x)+S(x);
S(x)
x
k
P(k<T(x)¬k+s) = P(K(x)=k\S(x)¬s)
=
kjs
q
x
=
k
p
x
s
q
x+k
:
P(K(x)=k\S(x)¬s) =
k
p
x
sq
x+k
= s
kj
q
x
= P(K(x)=k)P(S(x)¬s):
K(x) S(x)
P(S(x)¬s)=s
0<s<1;
S(x)
(0;1)
P(X> x+tjX> x) = P(T(x) > t)
[x]
r
8j>0q
[xj]+r+j
q
[x]+r
=q
x+r
:
r
3:7
2
p
[30]
3
q
[31]+1
2
p
[30]
=
l
[30]+2
r=2j=
l
32
l
[30]
=
33795
l
[30]
=j
33829
=0;99899
3
q
[31]+1
=1
l
[31]+1+3
r=2j=1
l
35
l
[31]+1
=1
33719
l
[31]+1
=j
33791
=0;00213: