chuong 1 -_sai_so
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7/25/2019 chuong 1 -_sai_so
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Chng 1
KHI NIM V
S GN NG
V SAI S
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sai lch gia gi tr gn ng v gitr chnh xc gi l sai s.
I. KHI NIM SAI S :
Ta c !"#$ %a$ %& :Sa$ %& g$' (h$)(
Sa$ %& %& !$*+ ,an -+
Sa$ %& /hng /h0/
Sa$ %& (nh ("0n
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Sa$ %& /hng /h0/ :C0c /hng /h0/ 23ng-4 g$'$ c0c ,5$ ("0n 67 (h+8( (h9ng !5 c0c
/hng /h0/ g$'$ ;/ < gn -=ng> ?@$/hng /h0/ c 1 %a$ %& nh;( -nh n5" -> %a$%& n5B g$ !5 %a$ %& /hng /h0/
Sa$ %& (nh ("0n : Tnh ("0n ,Dng ?0B (nh(h9ng ch< %E 2Fng 1 %& h+ h#n c0c ch %&
h"c !5? (Jn %&> c0c %a$ %& n5B (ch !B("ng L+0 (nh (nh ("0n g$ !5 %a$ %& (nh("0n haB %a$ %& !5? (Jn.
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II. CCH IOP QIRN SAI S :
Gi A l s chnh xc ca bi tn
! a gi l s gn ng ca A n"# n$ x%& x' A
() hi# a A
*i l+,ng - a / A gi l sai s th0c s0 ca s gn ng a
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1. Sa$ %& (+B*( -&$
1rng th0c t" 2 (h3ng tnh +4c A5 ta t67 8s 2+,ng a cng b9 cng tt th:
agi l %a$ %& (+B*( -&$ca s gn ng a
;) hi# A - a a
a A U a
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. %a$ %& (ng -&$ : W(nh (hX" YZ
!ai s t+,ng i ca s gn ng a l s 2+,ngatnh th 2? @Gi: s A - B
a - C.8D l s gn ng ca Ec nh sai s
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F Gi:i
F 1a c$- C.8D8HIJCKHLHCICKDJIJDCCKCILM C.8D N O P.P8
a- P.P8
QRt (hc
C.8D N O P.PP8J a- P.PP8J
a- P.C8KS
a- P.PPHJS
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T $ cUng 8 gi tr gn ng c$ thV c$
nhiW# sai s t#Xt i (hc nha#5 trng v 2?nX5 sai s P.PP8J l tt h,n
V 2F :Yh a - 8.K vZi sai s t+,ng i lP.8IS5 tnh sai s t#Xt i
a
- a [ a
- 8.K [ P.8I \8PP - P.PPIII
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]. Sa$ %& c^a ?_( h5? :
F Yh h7 X - ] ^x85 xI5 . . . 5 xn_F Q`i bi"n xic$ sai s xi. Ec nh sai s ca X
!ai s t#Xt i
!ai s t+,ng i
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> 2? @ Yh A - 8.P.PPI - P.8IC P.PP8 Y - 8C.PP P.P
1nh sai s t#Xt i8.x - a bI.X - IPa / 8Pb c
C.d - a bcD. t - aC IaIK
F Gi:iF 8. x- a b- P.PPI P.PP8 - P.PPCF I. X- IPa 8P b c- P.8F C. d- a c b b c- P.PI88F D. t- CaI Daa- P.PI
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> 2? @Yh ] - xCxXXC.i"t x-I.DCDLP.PPC5 X-I.JILK P.PPJI.
1nh sai s t#Xt i ]
FGi:i
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> 2? @ Tin tch +eng trfn ! - I
vZi
- C.8D
P.PPI v - .I
P.PP8 71nh sai s t#Xt i v t+,ng i ca !Gi:i @sai s t#Xt i
! - I[
I[
- ^.I_IxP.PPI IxC.8Dx.IxP.PP8- P.PKKPH
!ai s t+,ng i! - C.8D x ^.I_I- KJ.DJI!- !\ ! - P.8P8KS
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III. IOP QIRN S TH` HbN
! th& &hn a +4c biV# 2ijn 2+Zi 2*ng
a - a7a7N8... a8aP.aN8aNI... aNn
1. 5? (Jn %&
k7 trfn s l b 8 s cc ch s lm bn&h:i V +4c 8 s ngon gn h,n v gn ng vZia.
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Gi: s ta 7#n l7 trfn "n ch s lm th=( ^8 p ( p n_.
x9t I saN- a7a7N8... a8aP.aN8aNI... aN(a- a7a7N8... a8aP.aN8aNI...^aN(8_
chn s l7 trfn l aNhRc ath
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V 2F :
Yh a - DJ.8ICDJLKk7 trfn vZi I ch s lm
- aN- DJ.8I
k7 trfn vZi D ch s lm- a- DJ.8IC
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!ai s l7 trfn
Rt
1a c$
[ qE @ 1a c$ a.>X (hi l7 trfn sai
s s tng ln 5 nn trng tnh tn ta trnhl7 trfn cc &h9& tn tr#ng gian5 ch' l7trfn ("t u#: c#i cUng.
>X sai s l7 trfn @
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!ai s
gi:i
- 8KL.8IC / 8KL.8ICDJ - P.PPPPDD
>X - P.PPPPDD P.PPP8 - P.PPP8DD
> 2? @ Yh s YE A5 a - 8KL.8ICDJ l s
gn ng vZi sai s l P.PPP8. Gi
l s l7trfn ca a vZi D ch s lm. 1nh sai s ca svZi A
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i t&
i"t A c$ gi tr gn ng l a-C.ILP vZi sai s
t+,ng i l a- P.JDS. 1a l7 trfn a thnh vZi Ich s lm. 1nh sai s t#Xt i ca
!ai s
gi:i
- C.IL / C.ILP - P.PPP
>X - P.PPP P.PIPHC8I-P.PI8DC8I
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Ch= d :
1r+eng h4& l7 trfn trng b%t ng th=c5 ta2Ung (hi ni7 l7 trfn ln v l7 trfnx#ng
wk7 trfn ln @ - a5 & 2?ng ch cc s v" lZn h,n
wk7 trfn x#ng @ - aN
5 & 2?ng ch ccs v" nh h,n
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b y LK.JLKHl7 trfn x#ng ta +4c
b y LK.JL
> 2? @
a O 8C.HICJl7 trfn ln vZi I ch s lm ta +4c
a O 8C.HC
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i t& @
k7 trfn "n I ch s lm cc s trng ccbiV# th=c sa# @
a.a-8I.JLID b. a-8.DLJ
c.ap8I.KL8C 2. a8.ICD
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. Ch %& c nghea :
l nhng ch s tnh tz ch s (hc P #tin tz tri sang.
> 2? @
8P.IPPPC c$ L ch s c$ ngh{a
PP8ICD.CD c$ J ch s c$ ngh{a
P.P8PIPC c$ ch s c$ ngh{a8P.IPCPP c$ L ch s c$ ngh{a
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. Ch %& -0ng ($n :
Yh a A vZi sai s a .
Yh s a( gi l ch s ng tin n"#
ap 8P( \ IhaX ( lg ^Ia_
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> 2? @167 s ch s ng tin ca a8. a - L.CDJ vZi a- P.PPDD
I. a - L.CDJ vZi
a- P.PPJI
8. Yh s a(l ng tin n"#
( lg^P.PPKK_ - NI.PvX ta c$ D ch s ng tin L5 5 C5 D.
gi:i
I. ( lg^P.P8ID_ - N8.HPJvX ta c$ C ch s ng tin L5 5 C
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