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11/16/2016
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Bi ging Xc sut Thng k 2015 Nguyn Vn Tin
Xc sut Thng k
L thuyt Xc sut: xc sut, bin ngu nhin (1chiu, 2 chiu); lut phn phi xc sut thnggp
Thng k C bn: l thuyt mu, thng k mt, c lng, kim nh, hi quy
1 Bi ging Xc sut Thng k 2015 Nguyn Vn Tin
Ti liu v pp chng trnh
45 tit= 15 bui= 5 chng (7 chng theo cng chi tit ca trng)
Ti liu hc tp bt buc:Gio trnh Xc sut Thng k _L S ng
(C l thuyt v Bi tp in nm 2013)
Ti liu tham kho:
- Slide ging vin (nu cn thit)
- thi, p n cc kha trc
- Cc ti liu khc (tham kho c chn lc)
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Bi ging Xc sut Thng k 2015 Nguyn Vn Tin
Xc sut
Chng 1: Bin c v Xc sut
Chng 2: Bin ngu nhin
Chng 3: Mt s phn phi xc sut thngdng
3 Bi ging Xc sut Thng k 2015 Nguyn Vn Tin
Xc sut
Tnh xc sut c t nht 2 sinh vin cng ngysinh trong lp.
Tnh xc sut sinh vin u mn ny nu khnghc bi v gi s thi trc nghim ngu nhin
Lp c 60 sinh vin gm 20 nam, 40 n. Nulp ngu nhin 1 t gm 6 sinh vin th khnng c my sinh vin n l nhiu nht.
Trung bnh mt gi c 60 cuc gi n tng i.Xc sut trong 5 pht c ng 3 cuc gi?
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Bi ging Xc sut Thng k 2015 Nguyn Vn Tin
Thng k
Chng 4: c lng tham s
Chng 5: Kim nh gi thuyt thng k
Chng 6: Hi quy v tng quan (c thm)
5 Bi ging Xc sut Thng k 2015 Nguyn Vn Tin
Thng k
Trung bnh xe ca bn i c bao nhiu kmtrn 1 lt xng?
Nu ti ni trung bnh xe ca bn i c35km/l th kin ca bn nh th no?
D on chiu cao trung bnh ca sinh vinFTU2 K54 thuc khong no vi tin cy 95%?
Nu ni chiu cao sinh vin FTU2 K54 thp hn1m60 th c ng khng vi mc sai lm loi 1(mc ngha) 5%?
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Bi ging Xc sut Thng k 2015 Nguyn Vn Tin
Kim tra v nh gi
Chuyn cn: 10% = tham d lp + lm bi tp
Gia k: 20% = kim tra t lun hoc trcnghim, 60 pht
Cui k: 70% = thi t lun 75 pht
7 Bi ging Xc sut Thng k 2015 Nguyn Vn Tin
Tham kho v lin h
Tham kho thm:
https://onlinecourses.science.psu.edu/stat414/
https://onlinecourses.science.psu.edu/stat415/
Lin h:
nguyenvantien0405.wordpress.com
nguyenvantien0405.blogspot.com
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Bi ging Xc sut Thng k 2015 Nguyn Vn Tin
PHN 1
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BIN C V XC SUT
Bi ging Xc sut Thng k 2015 Nguyn Vn Tin
Ni dung cn nh
Cng thc cng, nhn tng qut
Cng thc Bernoulli
Cng thc Xc sut y
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Bi ging Xc sut Thng k 2015 Nguyn Vn Tin
Php th
Php th: l cc th nghim, quan st m ktqu ca n khng th d bo trc c.
K hiu: T.
Khng gian mu: l tp hp tt c cc kt quc th c ca php th
K hiu: ;
11 Bi ging Xc sut Thng k 2015 Nguyn Vn Tin
Bin c ngu nhin
Bin c s cp: kt qu ca php th. K hiu:wi
Bin c (ngu nhin): l tp con ca khng gianmu
K hiu: A, B, C, A1, A2
Bin c ngu nhin cha mt vi bin c s cpno .
Xc sut Thng k 2016 12
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Bi ging Xc sut Thng k 2015 Nguyn Vn Tin
Biu din
Khng gian mu: cha tt c cc kt qu caphp th
Bin c: tp con ca khng gian mu, cha mtvi kt qu ca php th
Xc sut Thng k 2016 13
BA
A v B l cc bin c trongkhng gian mu
B cha nhiu kt qu hn A Cc kt qu nm trong A
u nm trong B
Bi ging Xc sut Thng k 2015 Nguyn Vn Tin
V d 1
Tung mt ng xu. Quan st mt nga ln
1={S; N} hay 1={w1; w2}
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1w
12w
Bi ging Xc sut Thng k 2015 Nguyn Vn Tin
V d 2
T2: Tung hai ng xu phn bit (V d: 2k v5k). Quan st mt nga
2={SS; SN; NS; NN} hay 2={w1; w2; w3; w4}
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1w
4w
2w
3w
A
Pht biu bin c A?Bin c A xy ra khino?
Bi ging Xc sut Thng k 2015 Nguyn Vn Tin
V d 3
Tung 10 ng xu phn bit (10 loi khcnhau).
Hi: c bao nhiu kt qu? Biu din KG mu?
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Bi ging Xc sut Thng k 2015 Nguyn Vn Tin
V d 3
S kt qu: 1024=210
Biu din:
Hay:
Vi qui c: 0 l sp v 1 l nga
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3 1 2 10... ,ia a a a S N
3 1 2 10... 0,1ia a a a
Bi ging Xc sut Thng k 2015 Nguyn Vn Tin
Phn loi bin c
Bc khng th: l bc khng bao gi xy ra khithc hin T. K hiu:
Bc chc chn: l bc lun lun xy ra khi thchin T. K hiu:
Bin c rng khng cha mt bcsc no.
Bin c chc chn cha tt c bcsc ca phpth.
Xc sut Thng k 2016 18
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Bi ging Xc sut Thng k 2015 Nguyn Vn Tin
Quan h ko theo
Bin c A c gi l ko theo bin c B, k hiuAB, nu A xy ra th B cng xy ra
Ta ni A l bin c thun li cho B
Biu din:
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BA
Bi ging Xc sut Thng k 2015 Nguyn Vn Tin
V d 4
Mua ngu nhin 1 t v s
A: trng s
B: trng c c
Hi A ko theo B hay B ko theo A?
Xc sut Thng k 2016 20
Bi ging Xc sut Thng k 2015 Nguyn Vn Tin
Quan h tng ng
Bin c A tng ng vi bin c B nu A xyra th B xy ra v ngc li
K hiu: A=B
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A BA B
B A
Bi ging Xc sut Thng k 2015 Nguyn Vn Tin
V d 5
Mua ngu nhin 5 bng n
A: t nht 3 bng hng
B: nhiu nht 2 bng tt
A v B c tng ng?
Xc sut Thng k 2016 22
Bi ging Xc sut Thng k 2015 Nguyn Vn Tin
Tng (hp) hai bin c
Cho A, B l hai bc lin quan n php th T. Khi ,tng (hp) ca A v B l mt bin c, k hiu ABhay A+B
Bc ny xy ra khi:
t nht mt trong cc bc A, B xy ra
A hoc B xut hin trong php th
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A B
BA
Bi ging Xc sut Thng k 2015 Nguyn Vn Tin
V d 6
Mua ngu nhin 2 bng n.
A: bin c bng 1 hng
B: bin c bng 2 hng
A+B l bin c nh th no?
Xc sut Thng k 2016 24
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Bi ging Xc sut Thng k 2015 Nguyn Vn Tin
Tng (hp) cc bin c
A1, A2,,An l cc bc trong php th T.
Tng (hp) ca cc bc ny k hiu:
Bc ny xy ra khi t nht mt trong cc bc A1,A2,,An xy ra
Ta c:
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1 2 1 2... ...n nA A A hay A A A
1 2 1 2......
n nA A A A A A
Bi ging Xc sut Thng k 2015 Nguyn Vn Tin
Tch (giao) hai bin c
Cho A, B l hai bc lin quan n php th T. Khi, tch (giao) ca A v B l mt bin c, k hiuAB hay A.B
Bc ny xy ra khi c hai bc A, B cng xy ra ngthi trong php th
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A B
BA
Bi ging Xc sut Thng k 2015 Nguyn Vn Tin
V d 7
Sinh vin i thi 2 mn Ton Cao cp v Nguynl 2
A: sinh vin u Ton Cao cp
B: sinh vin u Nguyn l 2
A.B l bin c no?
Xc sut Thng k 2016 27 Bi ging Xc sut Thng k 2015 Nguyn Vn Tin
Tch (giao) cc bin c
A1, A2,,An l cc bc trong php th T.
Tch (giao) ca cc bc ny k hiu:
Bc ny xy ra khi tt c cc bc A1, A2,,An cngxy ra
Ta c:
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1 2 1 2... ...n nA A A hay A A A
1 2 1 2......
n nA A A A A A
Bi ging Xc sut Thng k 2015 Nguyn Vn Tin
Bin c i
Bin c i ca bin c A, k hiu l bin cxy ra khi v ch khi A khng xy ra.
Ta c: = \
V d:
Khi gieo mt con xc sc. Gi A: bc s chmchn th l bc s chm l
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1,2,3,4,5,6
2,4,6 1,3,5 \A AA
Bi ging Xc sut Thng k 2015 Nguyn Vn Tin
Hai bin c xung khc
Hai bin c A, B c gi l xung khc nu A vB khng th cng xut hin ng thi trongphp th.
Ngha l:
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AB
B
A
A v B xung khc
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Bi ging Xc sut Thng k 2015 Nguyn Vn Tin
Bin c hiu
Bin c hiu ca A v B, k hiu A\B l bin cxut hin khi A xut hin nhng B khng xuthin.
Ta c:
Ngha l:
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\ .A B AB
BA
A\B
Bi ging Xc sut Thng k 2015 Nguyn Vn Tin
V d 8
Sinh vin i thi 2 mn Ton Cao cp v Nguynl 2
A: sinh vin u Ton Cao cp
B: sinh vin u Nguyn l 2
M t cc bin c:
A\B; A+B
B\A; A + B; A + B ; A . B
Nhn xt g v: A + B v A . B
Xc sut Thng k 2016 32
Bi ging Xc sut Thng k 2015 Nguyn Vn Tin
Mt s tnh cht
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) . . .
) . .
)
) . .
)
) . .
) . . . .
i A A A A A A
A A A A A A
ii A B B A A B B A
iii A B C AB AC
iv A BC A B A C
v A A
vi A B A B A B A B
vii A B C A BC A BC A B C
Bi ging Xc sut Thng k 2015 Nguyn Vn Tin
V d 9
C 3 x th bn vo mc tiu
A, B, C l bc x th 1,2,3 bn trng
Biu din cc bin c sau theo A, B, C v cc phpton (cc quan h).
a) C ng mt x th bn trng
b) C nhiu nht mt x th bn trng
c) C t nht mt x th bn trng
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Bi ging Xc sut Thng k 2015 Nguyn Vn Tin
Kim tra cht lng 4 sn phm. Gi Ak l binc sn phm th k tt. Biu din cc bin csau theo Ak.
A l bc c 4 sn phm tt
B l bc c 3 sn phm tt
C l bin c c t nht 2 sn phm xu
D l bin c c t nht 1 sn phm tt
E l bin c c ti a 1 sn phm xu
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V d 10
Bi ging Xc sut Thng k 2015 Nguyn Vn Tin
N TP GII TCH T HP
Quy tc cng
Quy tc nhn
T hp chp k ca n phn t
Chnh hp chp k ca n phn t
Hon v ca n phn t
Xc sut Thng k 2016 36
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