bài giảng xác suất thống kê và ứng dụng tác giả: phan thanh hồng, trường...
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8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
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100%
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k
k
k
2n
1 3
k
2k n n
h
h
Xmax Xmin
k
Xmin Xmax
h
Xmin
Xmax
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k
k
2n
1 3
k
2k n n
h
h
Xmax Xmin
k
Xmin Xmax
h
Xmin
Xmax
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k
k
k
2n
1 3
k
2k n n
h
h
Xmax Xmin
k
Xmin Xmax
h
Xmin
Xmax
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Xmin Xmin h
Xmin h Xmin 2h
Xmin 2h Xmin 3h
xi
xi
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Xmin Xmin h
Xmin h Xmin 2h
Xmin 2h Xmin 3h
xi
xi
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K
7 27 65
Xmin 10 Xmax 29 h 29
10
7
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#
#
#
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#
#
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a, b
a, b
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#
#
#
49
500
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49
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29.8 33.3
29, 30, 31, 32, 33
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49
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5 20
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Bieu do tan so
Thoi gian
Tan
so
10 15 20 25 30 35
0
5
10
15
20
25
Bieu do tan suat
Thoi gian
Tan
suat
10 15 20 25 30 35
0.0
0
0.0
5
0.
10
0.1
5
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124/824
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125/824
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Bieu do tan so v da giac tan so Da giac tan so
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Thoi gian
Tan
so
10 15 20 25 30 35
0
5
10
15
20
25
10 15 20 25 30
0
5
10
15
20
Thoi gian
Tan
so
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55%
22%
11%
10%
2%
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8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
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55%
22%
11%
10%
2%
than da
55%
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55%
22%
11% 10%
2%
55%
nang luong hat nhan
22%khi ga tu nhien
11%
thuy dien
10%
dau hoa
2%
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100
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8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
135/824
do thi thanh
2
5
energy
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8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
136/824
1 2 3 4 5 6 7
0
5
10
15
20
gyindustrialretailhealth carefinancialtechnologyother
http://goforward/http://find/http://goback/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
137/824
1
2
3
4
5
6
7
0 5 10 15 20 25
energyindustrialretailhealth care
financialtechnologyother
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8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
138/824
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
139/824
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
140/824
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
141/824
http://goforward/http://find/http://goback/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
142/824
http://find/http://goback/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
143/824
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8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
144/824
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
145/824
200
1.0
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8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
146/824
value
0
50
100
150
0.5
0.6
0.7
0.8
0.9
T
an
suattich
luy
nhua do day vo quai nhan bac mau khac
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8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
147/824
y
y
y
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8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
148/824
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8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
149/824
33.5
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8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
150/824
10.0 10.5 11.0 11.5 12.0
32.0
32.5
33.0
3
LuongXB135
Donhot
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8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
151/824
y
x
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8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
152/824
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
153/824
http://find/http://goback/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
154/824
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
155/824
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
156/824
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
157/824
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
158/824
http://find/http://goback/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
159/824
http://find/http://goback/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
160/824
http://find/http://goback/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
161/824
http://find/http://goback/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
162/824
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
163/824
.
.
.
.
.
.
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8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
164/824
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
165/824
, , . . . ,
http://find/http://goback/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
166/824
. . . . .
.
http://find/http://goback/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
167/824
,
, . . . ,
,
, . . . ,
http://find/http://goback/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
168/824
.
.
.
.
.
.
.
.
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8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
169/824
.
.
.
.
.
.
.
.
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8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
170/824
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
171/824
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
172/824
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
173/824
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8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
174/824
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8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
175/824
Hinh a Hinh b Hinh c
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8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
176/824
Mo=Md=TB Mo
-
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
177/824
Mo=Md=TB Mo
-
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
178/824
Trung tam A
Thoi gian sua (ngay)
tan
so
0 2 4 6 8
0
2
4
6
8
Trung tam B
Thoi gian sua (ngay)
tan
so
0 2 4 6 8
0
2
4
6
8
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
179/824
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
180/824
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8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
181/824
http://goforward/http://find/http://goback/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
182/824
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
183/824
.
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8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
184/824
. .
. .
. .
.
.
.
.
.
.
.
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8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
185/824
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
186/824
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8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
187/824
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8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
188/824
.
.
.
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8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
189/824
.
.
.
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8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
190/824
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
191/824
%
%
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
192/824
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
193/824
.
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
194/824
%
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
195/824
.
.
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
196/824
.
.
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
197/824
%
Bieu do hop va rau cua mau 65 tgtt
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8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
198/824
10 15 20 25 30
%
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
199/824
%
%
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
200/824
%
http://goforward/http://find/http://goback/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
201/824
%
%
,
http://goforward/http://find/http://goback/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
202/824
%
,
.
%
,
http://goforward/http://find/http://goback/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
203/824
68%
++
95%
2 ++ 2
99.7%
3 ++ 3
http://goforward/http://find/http://goback/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
204/824
. .
,
. ,
.
%
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
205/824
,
. ,
.
%
,
. ,
.
.
%
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
206/824
%
,
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
207/824
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
208/824
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
209/824
http://goforward/http://find/http://goback/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
210/824
http://goforward/http://find/http://goback/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
211/824
http://goforward/http://find/http://goback/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
212/824
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
213/824
http://goforward/http://find/http://goback/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
214/824
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
215/824
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
216/824
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
217/824
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
218/824
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
219/824
http://find/http://goback/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
220/824
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
221/824
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
222/824
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
223/824
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
224/824
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
225/824
0, 1 1
0
0
1
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
226/824
1
A P A
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
227/824
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
228/824
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
229/824
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
230/824
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
231/824
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
232/824
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
233/824
S, N
1, 2, 3, 4, 5, 6
0, 1, 2, . . . , 100
0, 1, 2 . . .
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
234/824
S, N
1, 2, 3, 4, 5, 6
0, 1, 2, . . . , 100
0, 1, 2 . . .
A 2, 4, 6
T
G
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8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
235/824
G
TT,TG,GT,GG
B
B GT,TG,GG
A 2, 4, 6
T
G
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
236/824
G
TT,TG,GT,GG
B
B GT,TG,GG
A 2, 4, 6
T
G
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
237/824
TT,TG,GT,GG
B
B GT,TG,GG
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8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
238/824
A A
A
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
239/824
A A
A
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
240/824
n
A
A A
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
241/824
P
A
P S P N 1
2 0.5
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
242/824
52 A
A
P A 4
52
P S P N 1
2 0.5
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
243/824
52 A
A
P A 4
52
A
A
0
1
52
A 2
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
244/824
C252
A C24
P A C2
4
C252
0.0045
A
A
0
1
52
A
C2
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
245/824
C252
A C24
P A C2
4
C252
0.0045
A
A
0
1
52
A
C2
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
246/824
C252
A C24
P A C2
4
C252
0.0045
A m
n
n
m A
A
http://goforward/http://find/http://goback/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
247/824
A n
m
n
A
10 100 10000 6 47
5067
S
6 10 0.6 47 100 0.47 5067 10000 0.5067
S
0.5 P S 0.5
http://goforward/http://find/http://goback/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
248/824
10 100 10000 6 47
5067
S
6 10 0.6 47 100 0.47 5067 10000 0.5067
S
0.5 P S 0.5
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
249/824
http://goforward/http://find/http://goback/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
250/824
http://goforward/http://find/http://goback/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
251/824
A A
A A A
P A A
http://goforward/http://find/http://goback/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
252/824
A A
P A 1 P A
A
A
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
253/824
A A
P A C2
3
C27
0.143
P A 1 P A 0 857
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
254/824
P A 1 P A 0.857
A B
A B A
B A B A B P A B
A B
A
B
A
B A B A B P A B A
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
255/824
A B AB A B A B P A B A
B
A
B
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
256/824
A B A
B
P A B P A P B P A B A
B
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
257/824
A
B
P A B
P A 4
52 P B
26
52 P A B
2
52
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
258/824
P A B P A P B P A B 4
52
26
53
2
52
28
52 0.538
A
B
P A B
P A 4
52 P B
26
52 P A B
2
52
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
259/824
P A B P A P B P A B 4
52
26
53
2
52
28
52 0.538
A B
A B
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
260/824
A B
A B
P A B P A P B
A B
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
261/824
A1, A2, . . . , An
A1, A2, . . . , An A1 A2 An
A1 A2 An
Ai i 1, n
A1, A2, . . . , An A1 A2 An
A1A2 . . . An Ai i 1, n
A A A
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
262/824
A1, A2, . . . , An
i j Ai Aj
A1, A2, . . . , An
A1, A2, . . . , An A1 A2 An
A1 A2 An
Ai i 1, n
A1, A2, . . . , An A1 A2 An
A1A2 . . . An Ai i 1, n
A A A
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
263/824
A1, A2, . . . , An
i j Ai Aj
A1
A2
A3
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
264/824
n
A1, A2, . . . , An
P A1 A2 An P A1 P A2 P An
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
265/824
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
266/824
A B
A B P AB
A B
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
267/824
35 10
15 6 4
P T C
19
15
P T C 15 19 0.789
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
268/824
P T C 15 19 0.789
P T C 15 19 15 35
19 35
P T C
P C
35 10
15 6 4
P T C
19
15
P T C 15 19 0.789
http://find/http://goback/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
269/824
P T C 15 19 15 35
19 35
P T C
P C
35 10
15 6 4
P T C
19
15
P T C 15 19 0.789
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
270/824
P T C 15 19 15 35
19 35
P T C
P C
35 10
15 6 4
P T C
19
15
P T C 15 19 0.789
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
271/824
P T C 15 19 15 35
19 35
P T C
P C
35 10
15 6 4
P T C
19
15
P T C 15 19 0.789
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
272/824
P T C 15 19 15 35
19 35
P T C
P C
A B
P AB P
A
B
P B
P B 0
B A
AP A B
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
273/824
P B A P A B
P A
P A 0
P AB
A B
P A B P AB P B
P B A P A
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
274/824
1000
68.3%
62%
85%
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
275/824
1000
68.3%
62%
85%
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
276/824
1000
68.3%
62%
85%
http://goforward/http://find/http://goback/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
277/824
1000
68.3%
62%
85%
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
278/824
1000
C1
C2
S
V
P C1 0.683 P S 0.62 P C1 S 0.85
P C1 S P S P C1 S 0.62 0, 85 0.527
527 1000
http://goforward/http://find/http://goback/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
279/824
1000
C1
C2
S
V
P C1 0.683 P S 0.62 P C1 S 0.85
P C1 S P S P C1 S 0.62 0, 85 0.527
527 1000
http://goforward/http://find/http://goback/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
280/824
1000
C1
C2
S
V
P C1 0.683 P S 0.62 P C1 S 0.85
P C1 S P S P C1 S 0.62
0, 85
0.527
527 1000
http://goforward/http://find/http://goback/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
281/824
1000
C1
C2
S
V
P C1 0.683 P S 0.62 P C1 S 0.85
P
C1
S
P
S
P
C1
S
0.62
0, 85
0.527
527 1000
http://goforward/http://find/http://goback/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
282/824
1000
C1
C2
S
V
P C1 0.683 P S 0.62 P C1 S 0.85
P
C1
S
P
S
P
C1
S
0.62
0, 85
0.527
527 1000
http://goforward/http://find/http://goback/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
283/824
S V
C1
C2
http://goforward/http://find/http://goback/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
284/824
S V
C1
C2
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8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
285/824
A B
P AB P A P B A P B
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8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
286/824
A B P A B P A P B
http://goforward/http://find/http://goback/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
287/824
n
A1, A2, . . . , An
n
A1, A2, . . . , An
P A1A2 . . . An P A1 P A2 . . . P An
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
288/824
3
0.01 0.02 0.03
Ai i i 1, 2, 3
A
A1A2A3
A1A2A3
A1A2A3
A1 A2 A3
P A P
A1A2A3 A1A2A3 A1A2A3
P A1A2A3 P A1A2A3 P A1A2A3
P A1 P A2 P A3 P A1 P A2 P A3
P A1 P A2 P A3
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
289/824
1 2 3
0.99 0.02 0.03 0.01 0.98 0.03
0.01 0.02 0.97
0.0011
3
0.01 0.02 0.03
Ai i i 1, 2, 3
A
A1A2A3
A1A2A3
A1A2A3
A1 A2 A3
P A P
A1A2A3 A1A2A3 A1A2A3
P A1A2A3 P A1A2A3 P A1A2A3
P A1 P A2 P A3 P A1 P A2 P A3
P A1 P A2 P A3
http://goforward/http://find/http://goback/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
290/824
1 2 3
0.99 0.02 0.03 0.01 0.98 0.03
0.01 0.02 0.97
0.0011
A1, A2. . . . , An
A1 A2 An
Ai Aj i j
A, A
http://goforward/http://find/http://goback/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
291/824
Ai i A1, A2, A3
A1, A2. . . . , An H
P H
n
i 1
P HAi P Ai
P HA1 P A1 P HA2 P A2 P HAn P An
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
292/824
A1, A2. . . . , An H A1, H A2, . . . , H An
H H H A1 H A2 H An
P
H
P
H
A1
H
A2
H
An
P H A1 P H A2 P H An
P H A P A P H A P A P H A P A
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
293/824
P HA1 P A1 P HA2 P A2 P HAn P An
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
294/824
32%
Ai i i 1, 2
T
P T 0.32 P A1 P A2 0.5 P T A1 0.5
P T A2
A1 A2
P T P T A1 P A1 P T A2 P A2
0 5 0 5 P T A 0 5 0 32
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
295/824
0.5 0.5 P T A2 0.5 0.32
P T A2 0.32 0.25 0.5 0.14
A1, A2, . . . , An H
i 1, n
P Ai H P HAi P Ai
P H
P HAi P Ai
P HA1 P A1 P HA2 P A2 P HAn P An
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
296/824
P HAi P Ai P Ai H P H
P
Ai
H
P HAi P Ai
P H
P H P HA1 P A1 P HA2 P A2 P HAn P An
P Ai H P HAi P Ai
P H A P A P H A P A P H A P A
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
297/824
P Ai HP HA1 P A1 P HA2 P A2 P HAn P An
1
6
8
2 10 12
1
Ai
i
i
1, 2
X
P A1 X
P A1 H P
H
A1
P
A1
P HA1 P A1 P HA2 P A2
6 14 0 5
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
298/824
6 14 0.5
6 14 0.5 10 22 0.5 0.485
1
6
8
2 10 12
1
Ai
i
i
1, 2
X
P A1 X
P A1 H P
H
A1
P
A1
P HA1 P A1 P HA2 P A2
6 14 0.5
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
299/824
6 14 0.5
6 14 0.5 10 22 0.5 0.485
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
300/824
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
301/824
SS,SN,NS,NN
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
302/824
X X
SS,SN,NS,NN
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
303/824
X X
X
X
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
304/824
X
X
X
X
X
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
305/824
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
306/824
X
X
X pX x p x
p x X
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
307/824
X
X
X
X
p x
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
308/824
X
P(x)
0.0
0.1
0.2
0.3
0.4
0.5
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
309/824
X
0.5 0.0 0.5 1.0 1.5 2.0 2.5
0
0 p x 1
xp x 1
http://goforward/http://find/http://goback/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
310/824
X X
X X X X
2X X
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
311/824
X
x
x
xp x
X
2x
x
x X2p x
x
x2p x 2X
X X X
2
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
312/824
X 2x
X
X
p x
X 1 0.2 0 0.1 3 0.6 4 0.1 2
2X 1 2
0.2 02 0.1 32 0.6 42 0.1 22 3.2
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
313/824
f x
X X X
a, b
X a, b
P a X b
b
a
f x dx
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
314/824
X x P X x 0
f x
X X X
a, b
X a, b
P a X b
b
a
f x dx
http://goforward/http://find/http://goback/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
315/824
X x P X x 0
f x X
f x 0 x
f x 1
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
316/824
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
317/824
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
318/824
n
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
319/824
n
p
q 1 p
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
320/824
X
X n
X
X B n, p x
n
P X x p x Cxnpxqn x n!
x! n x !pxqn x
http://goforward/http://find/http://goback/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
321/824
3
0.51 X X
X B 3, 0.51
P X 2 3!
2!1!0.5120.491 0.382
P X 1 P X 1 P X 2 P X 3 0.88
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
322/824
0 1 2 3 4 5
0.
0
0.
2
0.
4
0.
6
x
p(x)
PP nhi thuc voi n=5, p=0.1
0 1 2 3 4 5
0.
05
0.
15
0.
25
x
p(x)
PP nhi thuc voi n=5, p=0.5
0 1 2 3 4 5
0.
0
0.
2
0.
4
0.
6
x
p(x)
PP nhi thuc voi n=5, p=0.9
0 5 10 15 20
0.
00
0.
10
0.
20
p(x)
PP nhi thuc voi n=20, p=0.2
0 10 20 30 40 50
0.
00
0.
04
0.
08
p(x)
PP nhi thuc voi n=50, p=0.5
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
323/824
x x
X X B n, p
X np, 2
X npq, X
npq
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
324/824
X B n, p
P X x
P X x
x P X x
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
325/824
X
x
P X x e
x
x!
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
326/824
X
X P
X X P 5
P X 3 e 553
3! 0.14
Y Y P 2.5
2
P Y 2 1 P Y 0 P Y 1 0.712
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
327/824
P Y 2 1 P Y 0 P Y 1 0.712
X X P 5
P X 3 e 553
3! 0.14
Y Y P 2.5
2
P Y 2 1 P Y 0 P Y 1 0.712
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
328/824
0 0 7
0.0 1.0 2.0 3.0
0.
0
0.
2
0.
4
0.
6
0.
8
x
p(x)
PP Poisson voi trung binh 0.1
0 2 4 6 8 10
0.
0
0.
1
0.
2
0.
3
0.
4
0.
5
0.
6
x
p(x)
PP Poisson voi trung binh 0.5
0 2 4 6 8 10
0.
00
0.
10
0.
20
x
p(x)
PP Poisson voi trung binh 2
0 5 10 15
0.
00
0.
05
0.
10
0.
15
x
p(x)
PP Poisson voi trung binh 5
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
329/824
X
X , 2
X , X
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
330/824
X P
P X x
P X x
x P X x
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
331/824
a b a b X
f x
1
b a a x b
0
X a, b X U a, b
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
332/824
x
f(x)
a b
1
((b a))
c d
P(c
-
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
333/824
X a, b
X a b
2 , X
b a
12
P
c
X
d
d c
b a
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
334/824
X
0 4
2.5
a 0 b 4 X
f x
1
4 0 x 4
0
2.5
P X 2.5 P 2.5 X 4 4 2.54 0
0.375
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
335/824
X
0 4
2.5
a 0 b 4 X
f x
1
4 0 x 4
0
2.5
P X 2.5 P 2.5 X 4 4 2.54 0
0.375
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8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
336/824
X U a, b
P X x
x P X x
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8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
337/824
X
f x 1
2e
x 2
22
X X N , 2
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8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
338/824
x
f((x))
1 2
Trung binh thay doi
x
f((x))
Phuong sai thay doi
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8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
339/824
X X
a, b
x a x b
x
f((x))
a b
P(a
-
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
340/824
a b
X
Z X
0 1
0 1
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8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
341/824
P a X b
P a X b
X N , 2
X N 6, 16 P 5 X 6.5
P 5 X 6.5 P 5 64
X 6
4
6.5 6
4 P 0.25 Z 0.13
P Z 0.13 P Z 0.25 Z N 0, 1
0.25 P Z 0.25 0.4
0.13
P
Z 0
.13 0
.552
P 5 X 6.5 0.552 0.4 0.152
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8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
342/824
P a X b
P a X b
X N , 2
X N 6, 16 P 5 X 6.5
P 5 X 6.5 P 5 64
X 6
4
6.5 6
4 P 0.25 Z 0.13
P Z 0.13 P Z 0.25 Z N 0, 1
0.25 P Z 0.25 0.4
0.13
P
Z 0
.13 0
.552
P 5 X 6.5 0.552 0.4 0.152
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8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
343/824
P a X b
P a X b
X N , 2
X N 6, 16 P 5 X 6.5
P 5 X 6.5 P 5 64
X 6
4
6.5 6
4 P 0.25 Z 0.13
P Z 0.13 P Z 0.25 Z N 0, 1
0.25 P Z 0.25 0.4
0.13
P
Z 0
.13 0
.552
P 5 X 6.5 0.552 0.4 0.152
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8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
344/824
Z
P Z z P Z z
P Z 0 P Z 0 0.5
P Z z 0.5 P 0 Z z z
P Z z 0.5 P 0 Z z z
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8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
345/824
X N , 2
P X x
x P X x
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8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
346/824
X
f x
e x
x
00
X E
X
X 1
, X
1
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8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
347/824
x
f(x)
=1 =4 =0.6
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8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
348/824
X E
P X x 1 e x
P a X b e a e b
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8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
349/824
f((x)) == e((x))
P(a
-
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
350/824
a b
1
2
X
X 1 1 2 0.5
P X 1 3 1 e1
3
0.5 1 e2 3 0.487
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8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
351/824
1
2
X
X 1 1 2 0.5
P X 1 3 1 e1
3
0.5 1 e2 3 0.487
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8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
352/824
1
2
X
X 1 1 2 0.5
P X 1 3 1 e1
3
0.5 1 e2 3 0.487
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8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
353/824
X E
P X x
x P X x
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8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
354/824
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8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
355/824
X X B n, p n p
np 5 nq 5 q 1 p X
np
npq
X B 50, 0.5 P X 24
np 50 0.5 25 5 nq 50 0.5 25 5
X 25
50 0.5 0.5 3.536
P X 24 P 23.5 X 24.5
X P 23.5 X 24.5 P 23.5 25
3.536 Z
24.5 25
3.536 P 0.42 Z 0.14 0.11
P X 24 0.11
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8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
356/824
P
20
X
30
P
21
X
30
P
20.5
X
30.5
P X 29 P 0.5 X 29.5
P X 35 P 36 X 50 P 35.5 X 50.5
P 18 X 42 P 19 X 41 P 18.5 X 41.5
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8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
357/824
X
5 X
X 10
8
P
X
8
P
X
8.5
P
Z
8.5 10
10
0.318
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8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
358/824
X
5 X
X 10
8
P
X
8
P
X
8.5
P
Z
8.5 10
10
0.318
http://goforward/http://find/http://goback/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
359/824
X X
FX x FX x P X x
x
X p x
FX x P X x
t x
p t
X f x
FX x P X x
x
f t dt
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8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
360/824
X X
FX x FX x P X x
x
X p x
FX x P X x
t x
p t
X f x
FX x P X x
x
f t dt
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8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
361/824
Y X Y x
y
X
x
Y
y
X Y
a, b E aX b aEX b V aX b a2V X E X Y EX EY
V X Y V X V Y X Y
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8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
362/824
Y X Y x
y
X
x
Y
y
X Y
a, b E aX b aEX b V aX b a2V X E X Y EX EY
V X Y V X V Y X Y
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8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
363/824
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
364/824
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
365/824
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
366/824
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
367/824
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
368/824
{
,
,
,
}
= +
+
+
= .
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8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
369/824
=
+
+
.
+
+
.
+
.
= .
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8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
370/824
Do thi tan suat cua tong the
x
18 19 20 21 22 23
0
.00
0.
05
0.
10
0.
15
0.
20
0.
25
Do thi tan suat cho tong the 6 trung binh mau
y
18 19 20 21 22 23
0
.00
0.
05
0.
10
0.
15
0.
20
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8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
371/824
/
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8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
372/824
=
=/
= /
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8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
373/824
Histogram of TongThe
TongThe
Density
0 1 2 3 4 5
0.0
0
0.0
5
0.1
0
0.1
5
0.2
0
Histogram of TrungBinhMau
TrungBinhMau
Density
2.0 2.2 2.4 2.6 2.8 3.0 3.2
0.0
0.5
1.0
1.5
2.0
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8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
374/824
=
=
(
/ . = .
. = .
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8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
494/824
: = : >
=
/
= .
. /
= .
= . . = . <
= .
.
= . > = .
. = . >
( >
) =
(
>
.
) =
.
>
.
=
.
>
. = .
http://find/ -
8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009
495/824
(
>
)
(
|
|)
=
/