Thong ke kinh doanh2
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Transcript of Thong ke kinh doanh2
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Chöông 4 Xaùc Suaát (Probability)Khaùi nieämPhöông phaùp tính xaùc suaátQuy taéc coäng xaùc suaátQuy taéc nhaân xaùc suaátCoâng thöùc tính xaùc suaát toaøn phaànCoâng thöùc BayesQuy taéc ñeám
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Khaùi nieäm
Xaùc suaát (Probability).Pheùp thö û(Experiment).Keát cuïc (Outcome).Bieán coá (Event).
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Phöông phaùp tính xaùc suaátPhöông phaùp khaùch quan
Phöông phaùp coå ñieån
Phöông phaùp thöïc nghieäm
Soá keát cuïc thuaän lôïi cho A
Toång soá keát cuïc ñoàng khaû naêngP(A)=
Soá laàn bieán coá A xuaát hieän trong quaù khöù
Toång soá quan saùtP(A)=
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Phöông phaùp chuû quanPhaùn ñoaùn caù nhaân.Kinh nghieäm.Yù kieán chuyeân gia.
Phöông phaùp tính xaùc suaát
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Qui taéc coäng xaùc suaát
Hai bieán coá goïi laø xung khaéc khi khoâng theåxaûy ra ñoàng thôøi trong moät pheùp thöû
Bieán coá xung khaéc
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A B
Coâng thöùc coäng ñaëc bieätP(A hoaëc B)= P(A) + P(B)
Qui taéc coäng xaùc suaát
Giaûn ñoà Venn : A, B xung khaéc
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ªBieán coá ñoái laäp
)(1)(1)()(
APAPAPAP
−=
=+A
A
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A, B khoâng xung khaéc Coâng thöùc coäng toång quaùt:
P(A hoaëc B)=P(A) + P(B) -P(A.B)
AvaøB
AB
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Qui taéc nhaân xaùc suaát
Bieán coá ñoäc laäp Coâng thöùc nhaân ñaëc bieät:
P(A.B) = P(A).P(B)
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Xaùc suaát coù ñieàu kieän.
Qui taéc nhaân xaùc suaát
0)()(
).()/(
≠
=
APAPBAPABP
Vôùi:
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Qui taéc nhaân xaùc suaát
Hai bieán coá A, B khoâng ñoäc laäp
Coâng thöùc nhaân xaùc suaát toång quaùt.
P(A.B) = P(A).P(B/A)
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Coâng thöùc tính xaùc suaát ñaày ñuû
Coâng thöùc tính xaùc suaát ñaày ñuû
BA1
A2
A3
A4
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Coâng thöùc:
Coâng thöùc tính xaùc suaát ñaày ñuû
∑=
=n
iii ABPAPBP
1)/().()(
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Coâng thöùc Bayes
Coâng thöùc Bayes
∑=
= n
iii
iii
ABPAP
ABPAPBAP
1)/().(
)/().()/(
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Qui taéc ñeám
Qui taéc nhaânSoá caùch ñeå hoaøn thaønh toaøn boä coâng vieäc
Chænh hôïp
n1.n2….nk
)!(!kn
nAkn −=
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kkn nA =
)!(!!
knknCk
n −=
Chænh hôïp laëp.
Toå hôïp.
Qui taéc ñeám
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Chöông 5 Bieán ngaãu nhieân vaøcaùc phaân phoái xaùc suaát thoâng
duïng.
Bieán ngaãu nhieân
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Bieán ngaãu nhieân
Khaùi nieämKyù hieäu:X,Y,.. Bieán ngaãu nhieân vaø x, y…trò soá cuûa
bieán ngaãu nhieân.Bieán ngaãu nhieân rôøi raïc.Bieán ngaãu nhieân lieân tuïc.
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Phaân phoái xaùc suaát
Phaân phoái xaùc suaát cuûa bieán ngaãu nhieân rôøi raïc.X x1 x2 … xn Coäng
Pi P1 P2 … Pn ∑Pi=1
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Ñaëc tröng cuûa bieán ngaãu nhieân
Trung bình (Kyø voïng-Expected)
Phöông sai (Variance)
∑=
==n
iii xPxXE
1)()(μ
∑=
−=n
iii xPx
1
22 )()( μσ
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Ñoä leäch tieâu chuaån
Ñaëc tröng cuûa bieán ngaãu nhieân
∑=
−=n
iii xPx
1
2 )()( μσ
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Phaân phoái xaùc suaát cuûa bieán ngaãu nhieân lieân tuïc
Phaân phoái xaùc suaát cuûa bieán ngaãu nhieân lieân tuïc
∫=⟨⟨b
a
dxxfbXaP ).()(
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f(x): laø haøm maät ñoä xaùc suaát phaûi thoûa 2 ñieàu kieän:
Phaân phoái xaùc suaát cuûa bieán ngaãu nhieân lieân tuïc
0)( ≥xf
∫+∞
∞−
= 1)()( xdxf
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Phaân phoái xaùc suaát thoâng duïng
Phaân phoái nhò thöùc.Trong moät pheùp thöû chæ coù 2 keát quaû: thaønh coâng hay khoâng thaønh coâng.Xaùc suaát thaønh coâng khoâng ñoåi ôû töøng pheùp thöû.Caùc pheùp thöû ñoäc laäp.
Xaùc suaát ñeå coù x laàn thaønh coâng trong n pheùp thöû:
xnxxn PPCxP −−= )1()(
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Ñaëc tröng cuûa phaân phoái nhò thöùc.
Trung bình:
Phöông sai:
Ñoä leäch tieâu chuaån:
PnXE .)( ==μ
)1(.2 PPn −=σ
)1(. PPn −=σ
Phaân phoái xaùc suaát thoâng duïng
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Phaân phoái sieâu boäi.Trong moät pheùp thöû chæ coù 2 keát quaû:thaønh coâng hay khoâng thaønh coâng.Xaùc suaát thaønh coâng khoâng coá ñònh.Caùc pheùp thöû khoâng ñoäc laäp.
Xaùc suaát ñeå coù x laàn thaønh coâng trong n pheùp thöû:
nN
xnSN
xS
CCCxP
−−=
.)(
Phaân phoái xaùc suaát thoâng duïng
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Ñaëc tröng cuûa phaân phoái sieâu boäi
Trung bình:
Phöông sai:
Ñoä leäch tieâu chuaån:
PnXE .)( ==μ
1)1(2
−−
−=N
nNPnPσ
1.)1(
−−
−=N
nNPnPσ
Phaân phoái xaùc suaát thoâng duïng
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Phaân phoái PoissonCoâng thöùc:
Ñaëc tröng cuûa phaân phoái Poisson:Trung bình:
Phöông sai:
Ñoä leäch tieâu chuaån:
!.)(xexP
x μμ −
=
PnXE .)( ==μ
Pn .2 =σ
Pn .=σ
Phaân phoái xaùc suaát thoâng duïng
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NGUYEÂN LYÙ TK KINH TEÁ
Phaân phoái chuaån
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Phaân phoái chuaånÑònh nghóa:
Phaân phoái cuûa bieán ngaãu nhieân lieân tuïcHaøm maät ñoä xaùc suaát cuûa X:
⟨+∞∞⟨−=−−
xexfx
2
2
2)(
21)( σ
μ
πσ
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Phaân phoái chuaån
Ñöôøng congphaân phoái chuaån
Mean Median Mode
X
f(X)
μ
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1.Ñoái xöùng2.
Xaáp xæ 68% giaù trò naèm trong khoaûng ±1σ so vôùi μ.Xaáp xæ 95% giaù trò naèm trong khoaûng ±2σ so vôùi μ.Xaáp xæ 99,73% giaù trò naèm trong khoaûng ±3σ so vôùi μ.
Tính chaát cuûa phaân phoái chuaån.
ModeM e ==μ
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Phaân phoái chuaån
μ x
f(x)
0
σ(μ+σ)(μ-σ)
68%
95%
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Phaân Phoái Chuaån
Vôùi caùc tham soá μ vaø σ thay ñoåi, ta coù caùc phaân phoái chuaån khaùc nhau
Hoï Phaân Phoái Chuaån
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Chuaån hoùa phaân phoái chuaån
Ñoåi bieán:
X~N(μ,σ2)
Haøm maät ñoä xaùc suaát cuûa Z:
σμ−
=xZ
2
2
.21)(
z
ezf−
=π
Z ~N (0,1)
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Ñöôøng cong phaân phoái chuaån ñôn giaûn
f(X)
μ
Z
σ
0Zμ =
1Zσ =
f(Z)
Phaân phoái chuaån Z coù trung bình baèng 0 vaø phöông sai baèng 1
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Tìm xaùc suaát
Xaùc suaát ñeå X nhaän giaù trò
trong khoaûng [c;d]!
c dX
f(X)
( ) ?P c X d≤ ≤ =
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Söû duïng baûng tính saün naøo?
Coù caû moät “hoï” phaân phoái chuaån, nghóa laø coù nhieàu baûng!
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Baûng tích phaân LaplaceZ 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.070.0 .0000 .0040 .0080 .0120 .0160 .0199 .0239 .02790.1 .0398 .0438 .0478 .0517 .0557 .0596 .0636 .06750.2 .0793 .0832 .0871 .0910 .0948 .0987 .1026 .10640.3 .1179 .1217 .1255 .1293 .1331 .1368 .1406 .14430.4 .1554 .1591 .1628 .1664 .1700 .1736 .1772 .18080.5 .1915 .1950 .1985 .2019 .2054 .2088 .2123 .2157
………1.0 .3413 .3438 .3461 .3485 .3508 .3531 .35541.1 .3643 .3665 .3686 .3708 .3729 .3749 .3770… … … … … … … … … …2.0 .4772 .4778 .4783 .4788 .4893 .4798 .4803…2.5 .4938 .4940 .4941 .4943 .4945 .4946 .4948
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Söû duïng baûng phaân phoái chuaån ñôn giaûn
0.0 .000 .0040 .080
.0398 .0438
0.2 .0793 .0832 .0871
0.3 .1179 .1217 .1255
.0478.02
0.1 .0478
Xaùc suaát
Chæ caàn söû duïng moät baûng 0 1Z Zμ σ= =
Z = 0.120
Z .00 .010.5000
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Ví duï
6.2 5 0.1210
XZ μσ− −
= = =
Phaân phoái chuaån Chuaån hoaùphaân phoái chuaån
10σ = 1Zσ =
5μ =6.2 X Z
0Zμ =0.12
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Ví duï: ( )2.9 7.1 .1664P X≤ ≤ =
10σ = 1Zσ =
5μ =7.1 X Z0Zμ =
0.21
2.9 5 7.1 5.21 .2110 10
X XZ Zμ μσ σ− − − −
= = = − = = =
2.9 0.21−
.0832.0832
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Ví duï: ( )8 .3821P X ≥ =
10σ = 1Zσ =
5μ =8 X Z0Zμ =
0.30
8 5 .3010
XZ μσ− −
= = =
.3821
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Vaøi öùng duïngÑöôïc bieát thôøi gian thanh toaùn caùc hoùa ñôn
cuûa khaùch haøng taïi moät coâng ty coù phaân phoái chuaån vôùi trung bình laø 18 ngaøy vaø ñoäleäch tieâu chuaån laø 4 ngaøy. Haõy tính:
1.Tæ leä hoùa ñôn coù thôøi gian thanh toaùn töø 12 ñeán 18 ngaøy.
2.Tæ leä hoùa ñôn coù thôøi gian thanh toaùn töø 20 ñeán 23 ngaøy.
3.Tæ leä hoùa ñôn coù thôøi gian thanh toaùn tröôùc 8 ngaøy.
4.Tæ leä hoùa ñôn quaù haïn thanh toaùn >30ngaøy
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Ví dụ 2
Chiều cao những người trưởng thành củamột địa phương giả sử có phân phối chuẩn
với trung bình bằng 163 cm và độ lệch tiêu chuẩn là 4,5 cm.
1. Tính tỉ lệ những người trưởng thành cóchiều cao trong khoảng (160, 165) cm
2. Tính tỉ lệ những người trưởng thành cóchiều cao >165 cm
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3. Tính tỉ lệ những người trưởng thành cóchiều cao <160 cm.
4. Tính tỉ lệ những người trưởng thành cóchiều cao trong khoảng (165,170) cm
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Duøng phaân phoái chuaån ñeå xaáp xæcho caùc phaân phoái xaùc suaát rôøi raïc
1.Xaáp xæ cho phaân phoái nhò thöùcX ~ B(n,P) N(μ,σ2)Söû duïng heä soá ñieàu chænh lieân tuïc:±0,5Ví duï:Ban quaûn lyù cuûa moät nhaø haøng lôùn
nhaän ñònh raèng 70% khaùch haøng môùi seõ quay trôû laïi. Trong tuaàn naøy, coù 80 thöïc khaùch ñeán duøng böõa laàn ñaàu. Haõy tính xaùc suaát ñeå ít nhaát coù 60 khaùch haøng seõ trôû laïi.
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2. Xaáp xæ cho phaân phoái sieâu boäi
Ñoåi bieán:
3. Xaáp xæ cho phaân phoái Poisson.
1)1(
−−
−
−=
NnNPnP
nPXZ