1
Working Paper Series
Department of Economics and Finance
Hong Kong Shue Yan University
Working Paper Series
September 2011
All Rights Reserved
ISBN: 978-988-18444-9-1
Copyright 2011 by Hong Kong Shue Yan University
Information on the Working Paper Series can be found on the last
page. Please address any comments and further
inquiries to:
Dr. Shu-kam Lee
Working Paper Coordinator
Department of Economics and Finance
Hong Kong Shue Yan University
10 Wai Tsui Crescent
Braemar Hill Road
North Point
Hong Kong
Fax: 2806-8044
Tel: 2806-5121 (Mr. Jeffery Chan)
Email: [email protected]
1
1
30 1
2 2002 7 4
49 (02/053) 2011630 (11/077) 1311
7
31,464
1 () 1960s (1970s1980s1990s)
2 http://bet.hkjc.com/marksix/default.aspx
2
(Descriptive Statistics) (Frequency Distribution)
(Hyper-geometric Distribution) (Goodness-of-Fit Test)
(Auto-correlation)
2
200
20 30
30 1936
1945
60 1912
3 4 1975
19755
14 6
1976 36
3 1950 60 1965 4 3 80 20 1990 12
4
5 () 1931
100 ( HK$200
HK$300)
1 10
1977
3
6 (Mark Six) 2
3 67
355 (3649)HK$2
3 (210)1982
19851995
20012005
2.1
2.1
1976 7 13 1-36 6 HK$2
1983 8 16 1-40 6 HK$2
1988 10 6 1-42 6 HK$2
1990 1 30 1-45 6 HK$2
1991 9 13 1-45 6 HK$4
1995 6 13 1-45 6 HK$5 HK$5,000,000
1996 6 11 1-47 6 HK$5 HK$5,000,000
2002 7 4 1-49 6 HK$5 HK$5,000,000
2010 11 9 1-49 6 HK$10 HK$8,000,000
(Lotto Ticket)
6
6 6
6
6 19923820027449
7 1995 5 2 2010 1
4
6
846%
25%15%6%
54%
(9,600)(640)(320)(40)
(9600 + 640 + 320 + 40
)7%2.2
2.22.38 (1311)
2.2
45%
HK$76,800
15%
HK$38,400
40%
HK$19,200
2.3 1311 9
HK$19,761,689 2005 6 18
HK$342,962,710 2011 5 20
HK$70,962,580 2003 9 12
11 2003 7 15
8 2011 4 28 5 17
HK$4,337,425 2010 3 30
241 2002 12 31
8 2010 11 9
9 2002 7 4 2011 6 30 1311
http://zh.wikipedia.org/wiki/%E7%A4%BE%E6%9C%83%E7%A6%8F%E5%88%A9%E7%BD%B2
5
HK$175,420 2011 6 23
241 2002 12 31
3
6
1 7
6 1
02/053 11/077 ( 1311) 02/053
11/077( 1311 ) 7 ( 1311
) 1311 7 = 9177
3.1 2002 7 4 2011 6 30
( 7867 9177 ) 1311 1- 49
1 7866
6
6 3.1
35 2 41
3 43 5 46
8 48 15 49
10
34 6
1
10
3.1
6
3.1 1311 6 1 9177
3.1 1311
1 2 3 4 5 6
7.01 14.07 21.17 28.54 35.57 42.82 24.67
0.15 0.20 0.23 0.23 0.21 0.16 0.39
6 13 21 29 37 44 24
1 9 18 30 39 49 10
5.56 7.41 8.18 8.15 7.43 5.81 14.20
30.95 54.91 66.86 66.48 55.22 33.71 201.51
1.75 -0.20 -0.57 -0.54 -0.08 1.33 -1.26
7
1.30 0.60 0.22 -0.16 -0.60 -1.20 0.04
34 39 40 41 40 34 48
1 2 3 5 8 15 1
35 41 43 46 48 49 49
1311 1311 1311 1311 1311 1311 1311
(Goodness of fit test)11
2 2
e
eo
f
ff2
2
0f
ef
2 1 ( df = n-1)
2
,df
1311 49
9177 (1311 7 ) 3.2
fo 1 49 fe 1 49
9177 49 =
187.2857 2 44.6056 (P-value)
0.612712, (>0.6127)
1311
11
Newbold (1995), pp 405-410. 12
Excel =CHIDIST(44.6056,48) 0.6127
8
3.2 1311 13 2
(fo)
(fe)
e
eo
f
ff2
1 193 187.2857 0.1743
2 184 187.2857 0.0576
3 171 187.2857 1.4161
4 194 187.2857 0.2407
5 196 187.2857 0.4055
203 187.2857 1.3185
7 195 187.2857 0.3178
8 184 187.2857 0.0576
9 215 187.2857 4.1011
10 216 187.2857 4.4024
11 177 187.2857 0.5649
12 183 187.2857 0.0981
13 199 187.2857 0.7327
14 196 187.2857 0.4055
15 181 187.2857 0.2110
16 177 187.2857 0.5649
17 185 187.2857 0.0279
18 186 187.2857 0.0088
19 173 187.2857 1.0897
20 181 187.2857 0.2110
21 186 187.2857 0.0088
22 216 187.2857 4.4024
23 177 187.2857 0.5649
24 200 187.2857 0.8631
25 162 187.2857 3.4139
(fo)
(fe)
e
e
f
ff2
0
26 183 187.2857 0.0981
27 174 187.2857 0.9425
28 179 187.2857 0.3666
29 180 187.2857 0.2834
30 198 187.2857 0.6129
31 191 187.2857 0.0737
32 176 187.2857 0.6801
33 187 187.2857 0.0004
34 167 187.2857 2.1972
35 196 187.2857 0.4055
36 189 187.2857 0.0157
37 185 187.2857 0.0279
38 198 187.2857 0.6129
39 187 187.2857 0.0004
40 198 187.2857 0.6129
41 191 187.2857 0.0737
42 200 187.2857 0.8631
43 187 187.2857 0.0004
44 161 187.2857 3.6892
45 186 187.2857 0.0088
46 167 187.2857 2.1972
47 164 187.2857 2.8952
48 198 187.2857 0.6129
49 205 187.2857 1.6755
9177 9176.9993 44.6056
(Autocorrelation)
(YT YT-1YT-2.Y3Y2Y1) k (YT-kYT-k-1
YT-k-2.Y3Y2Y1) 14 11 r r 1 k
r 0 k
13
14
n = T-k 2011 6 30 1311
5 2011 6 21 1306 n = 1311-5= 1306
9
3.3 (r)
1 0.021 0.041 0.014 0.007 0.018 -0.026 -0.021
2 -0.004 0.016 -0.009 0.005 -0.003 0.007 -0.013
3 0.018 0.048 0.012 -0.030 -0.028 -0.010 -0.004
4 0.020 0.087 0.019 0.017 0.002 -0.000 -0.020
5 0.022 -0.009 0.014 0.039 0.042 0.043 0.014
6 -0.002 0.007 -0.023 -0.005 0055 0.039 0.019
7 -0.009 -0.040 -0.044 -0.030 0.012 0.010 0.011
8 0.017 -0.004 -0.001 -0.018 -0.004 0.006 0.008
9 -0.039 -0.039 -0.050 -0.017 -0.023 0.044 -0.017
10 0.039 -0.009 -0.024 0.040 0.015 0.007 -0.005
1311 (1311 )
0.0667 15
3.3 70 69 0.0667(
02.0r ) r = 0.087 7
4 49
((1/49)
(1/48) (1/47) (1/46) (1/45) (1/44) = 9.932116447 10-11 ) 6
(6! = 6 5 4 3 2 1 = 720 )
1/13,983,816 ( 1/49C6)
15
Newbold (1995), Test for zero population correction 433-434 df =
1304 ( 1311-
-2) = 0.01 t- 2.5796 r=0.0667 r>0.0667,
99% Newbold (1995), Test for zero population correction
433-434
10
16
1/43
17
18
N S
N-S N (sampling
without replacement) n S
X S n-X (Hyper-geometric Distribution)19
);;/(
n
N
Xn
SN
X
S
nNSXP
P(X/S; N; n) = n X ()
N = ()
S = ( S=6
S=7)
N-S = (
)
n = ( 6 n = 6)
16
2011 8 28 #009
17
1/49 ( 1/481/471/461/45 1/44)
18
19
Newbold (1995), pp 163-166
11
X = ()
n-X =
n
N
=
)!(!
!
nNn
NCnN
6 P(X/S=6; N=49;n=6)
1 P(X/S=6;
N=49;n=6) 6 6
5 7 6 7
( 7C6 = 7) 1 6 () 6 ( 6C5 = 6)
5 1 () (6C5 / 7C6) P(X=5/S=7; N=49; n=6)
(6C4 / 7C5) (6C3 / 7C4)
4.1
4.1 49
6
6
49
1
6
49
0
42
6
6
)6;49;6/6(
nNSXP
816,983,13
1
5
+
6
49
5
6
6
49
0
42
6
7
6
7
5
6
)6;49;7/6(
6
7
5
6
nNSXP
636,330,2
1
5
6
49
1
43
5
6
)6;49;6/5(
nNSXP
84.200,54
1
4
+
53.196,22
1
12
6
49
1
42
4
6
6
49
1
42
5
7
5
7
4
6
)6;49;7/5(
5
7
4
6
nNSXP
4
6
49
2
43
4
6
)6;49;6/4(
nNSXP
4.032,1
1
3
+
6
49
2
42
3
6
6
49
2
42
4
7
4
7
3
6
)6;49;7/4(
4
7
3
6
nNSXP
07.812
1
3
6
49
3
43
3
6
)6;49;6/3(
nNSXP 7.56
1
4.2 1976 36 49
36
49 86.07%86.07%80.04%79.83%71.09%70.46%
57.66%
8 2011 4 28 2011 5 17
( 2.4) HK$85,618,703 HK$33,995,839
HK$342,962,710 2011 5 17 2011 4 28 10
13
4.2
1-36
1-40
1-42
1-45
1-47
1-49
1/1,947,792 1/3,838,380 1/5,245,786 1/8,145,060 1/10,737,573
1/13,983,816
1/324,632 1/639,730 1/874,297.67 1/1,357,510 1/1,789,595.5
1/2,330,636
1/10,821.07 1/18,815.59 1/24,286.05 1/34,807.95 1/43,648.67
1/54,200.84
1/4,477.68 1/7,754.30 1/9,991.97 1/14,289.58 1/17,895.96
1/22,196.53
1/298.51 1/456.14 1/555.11 1/732.80 1/872.97 1/1,032.4
1/239.88 1/363.48 1/440.82 1/579.31 1/688.31 1/812.07
1/23.99 1/32.07 1/36.74 1/44.56 1/50.36 1/56.7
5
(Gambling) (2000 11)
148
(gaming)
3 4
5.1
14
5.1 2003 2010
(25%)
(15%)
(6%)
(54%)
2003 5,287,332,310 1,321,833,078 793,099,847 317,239,939
2,855,159,447
2004 6,345,933,668 1,586,483,417 951,890,050 380,756,020
3,426,804,181
2005 6,418,759,532 1,604,689,883 962,813,930 385,125,572
3,466,130,147
2006 6,379,315,075 1,594,828,769 956,897,261 382,758,905
3,444,830,141
2007 6,717,127,531 1,679,281,883 1,007,569,130 403,027,652
3,627,248,867
2008 6,247,696,134 1,561,924,034 937,154,420 374,861,768
3,373,755,912
2009 6,096,638,397 1,524,159,599 914,495,760 365,798,304
3,292,184,734
2010 6,329,232,472 1,582,308,118 949,384,871 379,753,948
3,417,785,535
49,822,035,119 12,455,508,780 7,473,305,268 2,989,322,107
26,903,898,964
25%15% 6%
2002 7 4 2011 6 30 1311
54%
= ( ) + ( ) +
( ) + ( ) +
( ) + ( ) +
( )
1311 HK$31,074,864,809
HK$56,451,095,322 55.05%
54% 334 60%
2011 6 23 28.13%
2011 3 26 108.83%
15
HK$4,3059,569 HK$23,703,17720 0.55
0.91
5.1 2002 7 4 2011 6 30 1311
5.1 2002 7 4 2011 6 30 1311 (TT) (TP)
5.2 1311
X
1311 64.3%
54% 53.83% 30% 40%
6 6 2010 11 20 2010 12
11 2011 1 13 2011 1 29 2011 3 26 2011 4 21
49
20 (Coefficient of variation)
X
SDCV
16
21 49 HK$10 49C6 = HK$139,838,160 54%
22 1 6
258 630 135456 172206 2466286
23
5.2 2002 7 4 2011 6 30 1311
20% X 30% 23 1.75% 1.75%
30% X 40% 706 53.85% 55.61%
40% X 54% 114 8.70% 64.30%
54% X 60% 87 6.64% 70.94%
60% X 70% 86 6.56% 77.50%
70% X 80% 135 10.30% 87.80%
80% X 90% 131 9.99% 97.79%
90% X 100% 23 1.75% 99.54%
100% X 110% 6 0.46% 100.00%
1311 100% - -
6
21 49 HK$10 49C6 = HK$139,838,160 54% HK$75,512,606
22
49C6
23
49C6 4.1
17
(income redistribution)
24
Newbold, P. (1995), Statistics For Business and Economics,
4th
Edition, Prentice-Hall International.
(2000),
2011 7 http://bet.hkjc.com/marksix/default.aspx
2011 7 http://www.668999.com/jqgl.html
148 2011 7 http://www.legislation.gov.hk/chi/home.htm
334 2011 7 http://www.legislation.gov.hk/chi/home.htm
24 ()()()()()
()()()()()
18
The working paper series is a series of occasional papers funded
by the Research and Staff
Development Committee. The objective of the series is to arouse
intellectual curiosity and
encourage research activities. The expected readership will
include colleagues within Hong Kong
Shue Yan University, as well as academics and professionals in
Hong Kong and beyond.
Important Note
All opinions, information and/or statements made in the papers
are exclusively those of the authors.
Hong Kong Shue Yan University and its officers, employees and
agents are not responsible, in
whatsoever manner and capacity, for any loss and/or damage
suffered by any reader or readers of
these papers.
Department of Economics and Finance
Hong Kong Shue Yan University
