Chapter 6 - Sampling Distribution

 

Wtatfstfgs b`r Iusflkss alc Kg`l`hfgs  2tn Kcftf`l

Gnaptkr : Wahpdflj alc Wahpdflj Cfstrfiutf`ls

Wtatfstfgs b`r Iusflkss alc Kg`l`hfgs, 2k © 955: Ukars`l Kcugatf`l, Flg.

Gnap : 1

 

Gnaptkr J`ads Abtkr g`hpdktflj tnfs gnaptkr, y`u sn`udc ik aidk t`?  t`?   









Cksgrfik a sfhpdk ralc`h sahpdk alc wny sahpdflj fs fhp`rtalt Kxpdafl tnk cfbbkrklgk iktwkkl cksgrfptfvk alc flbkrkltfad statfstfgs Ckbflk tnk g`lgkpt `b a sahpdflj cfstrfiutf`l Cktkrhflk tnk hkal alc stalcarc ckvfatf`l b`r tnk sahpdflj cfstrfiutf`l `b tnk sahpdk hkal, ^ Cksgrfik tnk Gkltrad Dfhft Snk`rkh alc fts fhp`rtalgk

Wtatfstfgs b`r Iusflkss alc Kg`l`hfgs, 2k © 955: Ukars`l Kcugatf`l, Flg.

Gnap :-9

 

S``ds `b Iusflkss Wtatfstfgs 

Cksgrfptfvk statfstfgs 



G`ddkgtflj, prkskltflj, alc cksgrfiflj cata

Flbkrkltfad statfstfgs 

Crawflj g`lgdusf`ls alc/`r hamflj ckgfsf`ls g`lgkrlflj a p`pudatf`l iaskc `ldy `l sahpdk cata

Wtatfstfgs b`r Iusflkss alc Kg`l`hfgs, 2k © 955: Ukars`l Kcugatf`l, Flg.

Gnap :-7

 

U`pudatf`ls alc Wahpdks 

 A U`pudatf`l U`pudatf`l fs  fs tnk skt `b add ftkhs `r flcfvfcuads `b fltkrkst 



  Kxahpdks?  Kxahpdks? 

Add dfmkdy v`tkrs fl tnk lkxt kdkgtf`l  kdkgtf`l   Add parts pr`cugkc t`cay  Add sadks rkgkfpts b`r L`vkhikr  L`vkhikr 

 A Wahpdk Wahpdk fs  fs a suiskt `b tnk p`pudatf`l 

  Kxahpdks?

1555 v`tkrs skdkgtkc at ralc`h b`r fltkrvfkw

 A bkw parts skdkgtkc b`r ckstrugtfvk tkstflj Yalc`h rkgkfpts skdkgtkc b`r aucft

Gnap :-3

Wtatfstfgs b`r Iusflkss alc Kg`l`hfgs, 2k © 955: Ukars`l Kcugatf`l, Flg.  

U`pudatf`l vs. Wahpdk U`pudatf`l  

a i

gc

Wahpdk  

kb jn f om d h l

i

g

jf

l

  ` p q rs t u v w

 `

r

 

 

y 

x y

z

u

Wtatfstfgs b`r Iusflkss alc Kg`l`hfgs, 2k © 955: Ukars`l Kcugatf`l, Flg.

Gnap :-;

 

Zny Wahpdk0 





Dkss tfhk g`lsuhflj tnal g`lsuhflj tnal a gklsus Dkss g`stdy t` g`stdy t` achflfstkr tnal a gklsus Ft fs p`ssfidk t` `itafl statfstfgad rksudts `b a prkgfsf`l iaskc  iaskc `l sahpdks. subbfgfkltdy nfjn prkgfsf`l

Wtatfstfgs b`r Iusflkss alc Kg`l`hfgs, 2k © 955: Ukars`l Kcugatf`l, Flg.

Gnap :-2

 

Wfhpdk Yalc`h Wahpdks 







Kvkry `iokgt fl tnk p`pudatf`l nas al kquad gnalgk `b gnalgk `b ikflj skdkgtkc @iokgts ark skdkgtkc flckpklckltdy Wahpdks gal ik `itaflkc br`h a taidk `b ralc`h luhikrs `r g`hputkr ralc`h luhikr jklkrat`rs

 A sfhpdk ralc`h sahpd sahpdk k fs tnk fck fckad ad ajaflst wnfgn `tnkr sahpdk hktn`cs ark g`hparkc

Gnap :-:

Wtatfstfgs b`r Iusflkss alc Kg`l`hfgs, 2k © 955: Ukars`l Kcugatf`l, Flg.  

Flbkrkltfad Wtatfstfgs 

Hamflj statkhklts ai`ut a p`pudatf`l iy kxahflflj sahpdk rksudts

statfstfgs   Wahpdk statfstfgs (ml`wl)

U`pudatf`l parahktkrs 

Flbkrklgk   Flbkrklgk

(ulml`wl, iut gal ik kstfhatkc br`h  

Wahpdk

U`pudatf`l

sahpdk kvfcklgk)

Wtatfstfgs b`r Iusflkss alc Kg`l`hfgs, 2k © 955: Ukars`l Kcugatf`l, Flg.

Gnap :->

 

Flbkrkltfad Wtatfstfgs Crawflj g`lgdusf`ls alc/`r hamflj ckgfsf`ls g`lgkrlflj a p`pudatf`l p`pudatf`l  iaskc `l sahpdk sahpdk rksudts.  rksudts. 

Kstfhatf`l 



k.j., Kstfhatk tnk p`pudatf`l hkal wkfjnt usflj tnk sahpdk hkal wkfjnt

Nyp`tnksfs Skstflj 

k.j., [sk sahpdk kvfcklgk t` tkst tnk gdafh tnat tnk p`pudatf`l hkal wkfjnt fs 195 p`ulcs

Wtatfstfgs b`r Iusflkss alc Kg`l`hfgs, 2k © 955: Ukars`l Kcugatf`l, Flg.

Gnap :-6

 

Wahpdflj Cfstrfiutf`ls 

 A sahpdflj cfstrfiutf`l fs cfstrfiutf`l fs a cfstrfiutf`l `b add `b tnk p`ssfidk vaduks `b a statfstfg b`r a jfvkl sfzk sahpdk skdkgtkc br`h a p`pudatf`l

Gnap :-15

Wtatfstfgs b`r Iusflkss alc Kg`l`hfgs, 2k © 955: Ukars`l Kcugatf`l, Flg.  

Gnaptkr @utdflk

Wahpdflj Cfstrfiutf`ls

Wahpdflj Cfstrfiutf`l `b Wahpdk Hkal

Wahpdflj Cfstrfiutf`l `b Wahpdk Ur`p`rtf`l

Wahpdflj Cfstrfiutf`l `b Wahpdk Rarfalgk

Gnap :-11

Wtatfstfgs b`r Iusflkss alc Kg`l`hfgs, 2k © 955: Ukars`l Kcugatf`l, Flg.  

Wahpdflj Cfstrfiutf`ls `b  Wahpdk Hkals

Wahpdflj Cfstrfiutf`ls

Wahpdflj Cfstrfiutf`l `b Wahpdk Hkal

Wahpdflj Cfstrfiutf`l `b Wahpdk Ur`p`rtf`l

Wahpdflj Cfstrfiutf`l `b Wahpdk Rarfalgk

Gnap :-19

Wtatfstfgs b`r Iusflkss alc Kg`l`hfgs, 2k © 955: Ukars`l Kcugatf`l, Flg.  

Ckvkd`pflj a Wahpdflj Cfstrfiutf`l 

Assuhk tnkrk fs a p`pudatf`l … A





U`pudatf`l sfzk L83 Yalc`h varfaidk, ^, fs ajk ajk `b  `b flcfvfcuads



Raduks `b ^? 1>, 95, 99, 93 (ykars) 93 (ykars)

I

G

C

Gnap :-17

Wtatfstfgs b`r Iusflkss alc Kg`l`hfgs, 2k © 955: Ukars`l Kcugatf`l, Flg.  

Ckvkd`pflj a Wahpdflj Cfstrfiutf`l (g`ltflukc)

Wuhhary Hkasurks b`r tnk U`pudatf`l  U`pudatf`l Cfstrfiutf`l? Cfstrfiutf`l?

  ^ δ



U(x)

f

L 1>  95  99  93 3

(^  δ)    χ f

L

.9;

 91  5

9

 9.972

 

1>

95

99

93

 

A

I

G

C

[lfb`rh Cfstrfiutf`l

x

Gnap :-13

Wtatfstfgs b`r Iusflkss alc Kg`l`hfgs, 2k © 955: Ukars`l Kcugatf`l, Flg.  

Ckvkd`pflj a Wahpdflj Cfstrfiutf`l (g`ltflukc)

L`w g`lsfckr add p`ssfidk sahpdks `b sfzk l 8 9 lc

st

9

1   is

1>

 @iskrvatf`l

95

99

12 Wahpdk

93

Hkals

1> 1>,1> 1>,95 1>,99 1>,93 95 95,1> 95,95 95,99 95,93

1st  9lc @iskrvatf`l is

1>

95

99

93

1>

99 99,1> 99,95 99,99 99,93 93 93,1> 93,95 93,99 93,93 12 p`ssfidk sahpdks (sahpdflj wftn rkpdagkhklt)

1> 16 95 91 95 16 95 91 99 99

95 91 99 97

93

91 99 97 93

Gnap :-1;

Wtatfstfgs b`r Iusflkss alc Kg`l`hfgs, 2k © 955: Ukars`l Kcugatf`l, Flg.  

Ckvkd`pflj a Wahpdflj Cfstrfiutf`l (g`ltflukc)

Wahpdflj Cfstrfiutf`l `b Add Wahpdk Hkals

Wahpdk Hkals

12 Wahpdk Hkals 1st  9lc @iskrvatf`l i s 1> 95 99 93 1>

1> 16 95 91 95 16 95 91 99 99

95 91 99 97

93

91 99 97 93

Cfstrfiutf`l

 P  U(^)  U(^)  .7 .9 .1 5

1> 16

95 91 99 97

(l` d`ljkr ulfb`rh)

93

 P  ^

Gnap :-12

Wtatfstfgs b`r Iusflkss alc Kg`l`hfgs, 2k © 955: Ukars`l Kcugatf`l, Flg.  

Ckvkd`pflj a Wahpdflj Cfstrfiutf`l (g`ltflukc)

Wuhhary Hkasurks `b tnfs Wahpdflj Cfstrfiutf`l?

^

 L

K(^) 

f

1>   16  91    93 91 δ    12

( ^f  δ) χ^ 



 

9

L

(1> - 91)9  (16 - 91)9    (93 - 91)9 12

 1.;>

Gnap :-1:

Wtatfstfgs b`r Iusflkss alc Kg`l`hfgs, 2k © 955: Ukars`l Kcugatf`l, Flg.  

G`hparflj tnk U`pudatf`l wftn fts Wahpdflj Cfstrfiutf`l Wahpdk Hkals Cfstrfiutf`l l89

U`pudatf`l L83

δ  91   χ  1.;>

δ  91   χ  9.972

^

 P  U(^) .7

U(^) .7

.9

.9

.1

.1

5

5 1>     1>

  A

95   95

I

99   99

G

93

C

^

1> 16

^

95 91 99 97

93

 P  ^

Wtatfstfgs b`r Iusflkss alc Kg`l`hfgs, 2k © 955: Ukars`l Kcugatf`l, Flg.

Gnap :-1>

 

_-vaduk b`r Wahpdflj Cfstrfiutf`l `b tnk Hkal 

_-vaduk b`r tnk sahpdflj cfstrfiutf`l `b ^ ?

_  ( ^  δ)  ( ^ χ δ) χ^ l ^ 8 sahpdk hkal

wnkrk?

δ 8 p`pudatf`l hkal  

χ 8 p`pudatf`l stalcarc ckvfatf`l l 8 sahpdk sfzk

Gnap :-16

Wtatfstfgs b`r Iusflkss alc Kg`l`hfgs, 2k © 955: Ukars`l Kcugatf`l, Flg.  

Bflftk U`pudatf`l G`rrkgtf`l 

Fb tnk sahpdk sfzk l fs l`t shadd g`hparkc t` tnk p`pudatf`l sfzk L , tnkl usk

_

( ^  δ) χ l

Ll L 1

Gnap :-95

Wtatfstfgs b`r Iusflkss alc Kg`l`hfgs, 2k © 955: Ukars`l Kcugatf`l, Flg.  

Wahpdflj Cfstrfiutf`l Ur`pkrtfks



L`rhad U`pudatf`l Cfstrfiutf`l

δx    δ   (f.k.

x fs ulifaskc )  

δ

x

δx

x

L`rhad Wahpdflj Cfstrfiutf`l (nas tnk sahk hkal)

Gnap :-91

Wtatfstfgs b`r Iusflkss alc Kg`l`hfgs, 2k © 955: Ukars`l Kcugatf`l, Flg.  

Wahpdflj Cfstrfiutf`l Ur`pkrtfks (g`ltflukc) 

B`r sahpdflj wftn rkpdagkhklt? rkpdagkhklt?   As l flgrkasks,

Darjkr sahpdk sfzk

χ x ckgrkasks Whaddkr sahpdk sfzk

δ

x

Gnap :-99

Wtatfstfgs b`r Iusflkss alc Kg`l`hfgs, 2k © 955: Ukars`l Kcugatf`l, Flg.  

Gkltrad Dfhft Snk`rkh  As tnk sahpdk sfzk jkts darjk kl`ujn…

l↑

tnk sahpdflj cfstrfiutf`l ikg`hks adh`st l`rhad rkjarcdkss `b snapk `b p`pudatf`l

x

Gnap :-97

Wtatfstfgs b`r Iusflkss alc Kg`l`hfgs, 2k © 955: Ukars`l Kcugatf`l, Flg.  

Fb tnk U`pudatf`l fs l`t l`t L`rhad  L`rhad (g`ltflukc) U`pudatf`l Cfstrfiutf`l

Wahpdflj cfstrfiutf`l pr`pkrtfks? Gkltrad Sklcklgy

δx  δ Rarfatf`l

χx  χ l

x

δ Wahpdflj Cfstrfiutf`l (ikg`hks l`rhad as l flgrkasks) Whaddkr sahpdk sfzk

Darjkr sahpdk sfzk

x

δx Wtatfstfgs b`r Iusflkss alc Kg`l`hfgs, 2k © 955: Ukars`l Kcugatf`l, Flg.

Gnap :-93

 

N`w Darjk fs Darjk Kl`ujn0 



B`r h`st cfstrfiutf`ls, l < 9; 9;   wfdd jfvk a sahpdflj cfstrfiutf`l tnat fs lkardy l`rhad B`r l`rhad p`pudatf`l cfstrfiutf`ls, tnk sahpdflj cfstrfiutf`l `b tnk hkal fs adways l`rhaddy cfstrfiutkc

Wtatfstfgs b`r Iusflkss alc Kg`l`hfgs, 2k © 955: Ukars`l Kcugatf`l, Flg.

Gnap :-9;

 

Kxahpdk 



Wupp`sk a p`pudatf`l nas hkal δ 8 > alc > alc stalcarc ckvfatf`l χ 8 7. 7. Wupp`sk a ralc`h 72 fs  fs skdkgtkc. sahpdk `b sfzk l 8 72 Znat fs tnk pr`iaifdfty tnat tnk sahpdk hkal hkal fs  fs iktwkkl :.> alc >.90

Gnap :-92

Wtatfstfgs b`r Iusflkss alc Kg`l`hfgs, 2k © 955: Ukars`l Kcugatf`l, Flg.  

Kxahpdk (g`ltflukc)

W`dutf`l? 







Kvkl fb tnk p`pudatf`l fs l`t l`rhaddy cfstrfiutkc, tnk gkltrad dfhft tnk`rkh gal ik uskc (l < 9;) … s` tnk sahpdflj cfstrfiutf`l `b appr`xfhatkdy l`rhad … wftn hkal

x

fs

8 >

δx …alc stalcarc ckvfatf`l 

χ χx

7

 l   72  5.;

Gnap :-9:

Wtatfstfgs b`r Iusflkss alc Kg`l`hfgs, 2k © 955: Ukars`l Kcugatf`l, Flg.  

Kxahpdk (g`ltflukc)

  W`dutf`l (g`ltflukc)?  U(:.> δ

 ^

   :.> - >

 >.9)

U 7

 

72



δ^ -δ χ

l



  >.9 - >  7

 72  

 U(-5.;  _  5.;)  5.7>75 U`pudatf`l Cfstrfiutf`l 0

Wahpdflj Cfstrfiutf`l

000

00

0 0 0

δ>

0

0

Wtalcarc L`rhad Cfstrfiutf`l

Wahpdk

0

^

.161; +.161;

Wtalcarcfzk

:.>

δ^    >

>.9

x

-5.; δ

z

   5 5.;

_

Wtatfstfgs b`r Iusflkss alc Kg`l`hfgs, 2k © 955: Ukars`l Kcugatf`l, Flg.

Gnap :-9>

 

 Aggkpta  Aggkptalgk lgk Fltkrvads Fltkrvads 

J`ad? cktkrhflk a raljk wftnfl wnfgn sahpdk hkals ark dfmkdy t` `ggur, jfvkl a p`pudatf`l hkal alc varfalgk 





Iy tnk Gkltrad Dfhft Snk`rkh, wk ml`w tnat tnk cfstrfiutf`l `b ^ fs appr`xfhatkdy appr`xfhatkdy l`rhad fb l fs darjk darjk kl`ujn, kl`ujn, wftn hkal δ alc stalcarc ckvfatf`l χ ^ Dkt zα/9 ik tnk z-vaduk tnat dkavks arka α/9 fl tnk uppkr tafd `b tnk l`rhad cfstrfiutf`l (f.k., tnk fltkrvad - z α/9 t` zα/9 klgd`sks pr`iaifdfty 1 ‗ α) Snkl

δ z  

/9

 

χ^

  fs tnk tnk fltkrvad tnat flgducks ^ wftn wftn pr`iaifdfty 1 ‗ α

Gnap :-96

Wtatfstfgs b`r Iusflkss alc Kg`l`hfgs, 2k © 955: Ukars`l Kcugatf`l, Flg.  

Wahpdflj Cfstrfiutf`ls `b  Wahpdk Ur`p`rtf`ls

Wahpdflj Cfstrfiutf`ls

Wahpdflj `b Cfstrfiutf`l Wahpdk Hkal

Wahpdflj `b Cfstrfiutf`l Wahpdk Ur`p`rtf`l

Wahpdflj `b Cfstrfiutf`l Wahpdk Rarfalgk

Wtatfstfgs b`r Iusflkss alc Kg`l`hfgs, 2k © 955: Ukars`l Kcugatf`l, Flg.

Gnap :-75

 

U`pudatf`l Ur`p`rtf`ls, U   U 8 tnk pr`p`rtf`l `b tnk p`pudatf`l navflj s`hk gnaragtkrfstfg 

 

Wahpdk pr`p`rtf`l  pr`p`rtf`l (U) pr`vfcks al kstfhatk `b U?

^ l



U   ˂

˂



5≣ U ≣1  U nas a ifl`hfad cfstrfiutf`l, cfstrfiutf`l , iut gal ik appr`xfhatkc iy a l`rhad cfstrfiutf`l wnkl lU(1 ‗ U) < 6 ˂

˂



luhikr `b ftkhs fl tnk sahpdk navflj tnk gnaragtkrfstfg `b fltkrkst  sahpdk sfzk

Gnap :-71

Wtatfstfgs b`r Iusflkss alc Kg`l`hfgs, 2k © 955: Ukars`l Kcugatf`l, Flg.  

\

Wahpdflj Cfstrfiutf`l `b U 

L`rhad appr`xfhatf`l? Wahpdflj Cfstrfiutf`l U(U) ˂

.7 .9 .1  5   5

Ur`pkrtfks?  

K(U )  p ˂

alc

.9

.3

.2

>

1 U

^  U(1 U)   χ U  Rar    l  l  9 ˂

(wnkrk U 8 p`pudatf`l pr`p`rtf`l)

˂

Gnap :-79

Wtatfstfgs b`r Iusflkss alc Kg`l`hfgs, 2k © 955: Ukars`l Kcugatf`l, Flg.  

_-Raduk b`r Ur`p`rtf`ls Wtalcarcfzk U t` a _ vaduk wftn tnk b`rhuda? ˂

U U U U _  χU   U(1  U) ˂

˂

˂

l

Wtatfstfgs b`r Iusflkss alc Kg`l`hfgs, 2k © 955: Ukars`l Kcugatf`l, Flg.

Gnap :-77

 

Kxahpdk 

Fb tnk truk pr`p`rtf`l `b v`tkrs wn` supp`rt s upp`rt Ur`p`sftf`l A fs U 8 .3, wnat fs tnk pr`iaifdfty tnat a sahpdk `b sfzk 955 yfkdcs a sahpdk pr`p`rtf`l iktwkkl .35 alc .3;0



f.k.? fb U 8 .3 alc l 8 955, wnat fs  

U(.35 ≣ U ≣ .3;) 0 ˂

Gnap :-73

Wtatfstfgs b`r Iusflkss alc Kg`l`hfgs, 2k © 955: Ukars`l Kcugatf`l, Flg.  

Kxahpdk (g`ltflukc) 

 

fb U 8 .3 alc l 8 955, wnat fs

Bflc χ ? U ˂

G`lvkrt t` stalcarc l`rhad?

χU ˂

 

U(.35 ≣ U ≣ .3;) 0



U(1 U) .3(1 .3)   l 955

˂

 .57323

.3;  .35   .35  .35   U(.35  U  .3;)  U _  .57323     .57323 ˂

 U(5  _  1.33)

Gnap :-7;

Wtatfstfgs b`r Iusflkss alc Kg`l`hfgs, 2k © 955: Ukars`l Kcugatf`l, Flg.  

Kxahpdk (g`ltflukc) 

 

fb p 8 .3 alc l 8 955, wnat fs  

U(.35 ≣ U ≣ .3;) 0 ˂

[sk stalcarc l`rhad taidk?

U(5 ≣ _ ≣ 1.33) 8 .39;1 Wtalcarcfzkc L`rhad Cfstrfiutf`l

Wahpdflj Cfstrfiutf`l

.39;1 Wtalcarcfzk

.35

.3;

˂

U

5

1.33

_

Gnap :-72

Wtatfstfgs b`r Iusflkss alc Kg`l`hfgs, 2k © 955: Ukars`l Kcugatf`l, Flg.  

Wahpdflj Cfstrfiutf`ls `b  Wahpdk Ur`p`rtf`ls

Wahpdflj Cfstrfiutf`ls

Wahpdflj `b Cfstrfiutf`l Wahpdk Hkal

Wahpdflj `b Cfstrfiutf`l Wahpdk Ur`p`rtf`l

Wahpdflj `b Cfstrfiutf`l Wahpdk Rarfalgk

Gnap :-7:

Wtatfstfgs b`r Iusflkss alc Kg`l`hfgs, 2k © 955: Ukars`l Kcugatf`l, Flg.  

Wahpdk Rarfalgk 

Dkt x1, x9, . . . , xl ik a ralc`h sahpdk br`h a p`pudatf`l. Snk sahpdk varfalgk fs varfalgk fs

s9 

1

l

 l 1

(x f  x)9

f1





tnk squark r``t `b tnk sahpdk varfalgk fs gaddkc tnk sahpdk stalcarc ckvfatf`l tnk sahpdk varfalgk fs cfbbkrklt b`r cfbbkrklt ralc`h sahpdks br`h tnk sahk p`pudatf`l

Wtatfstfgs b`r Iusflkss alc Kg`l`hfgs, 2k © 955: Ukars`l Kcugatf`l, Flg.  

Wahpdflj Cfstrfiutf`l `b  Wahpdk Rarfalgks 

Snk sahpdflj cfstrfiutf`l `b s9 nas hkal χ9

K(s 9  )  χ 9 



Fb tnk p`pudatf`l cfstrfiutf`l cfstrfiutf`l fs l`rhad, tnkl 3 9χ Rar(s 9 )  l 1 Fb tnk p`pudatf`l cfstrfiutf`l cfstrfiutf`l 9 fs l`rhad tnkl (l - 1)s χ9 nas a 9 cfstrfiutf` cfstrfiutf`l l wftn l ‗ 1 ckjrkks `b brkkc`h

Gnap :-7>

Gnap :-76

Wtatfstfgs b`r Iusflkss alc Kg`l`hfgs, 2k © 955: Ukars`l Kcugatf`l, Flg.  

Snk Gnf-squark Cfstrfiutf`l 



Snk gnf-squark cfstrfiutf`l fs cfstrfiutf`l fs a bahfdy `b cfstrfiutf`ls, ckpklcflj `l ckjrkks `b brkkc`h? c.b. 8 l ‗ 1

9 5 3 > 19 12 95 93 9>  

c.b. 8 1 

9 5 3 > 19 12 95 93 9>  

c.b. 8 ;

5 3 > 19 12 95 93 9>

c.b. 8 1;

Skxt Saidk : : g`ltafls  g`ltafls gnf-squark pr`iaifdftfks

 9

Wtatfstfgs b`r Iusflkss alc Kg`l`hfgs, 2k © 955: Ukars`l Kcugatf`l, Flg.  

Ckjrkks `b Brkkc`h (cb) Fcka? Luhikr  Luhikr `b `iskrvatf`ls tnat ark brkk t` vary Fcka?   abtkr sahpdk hkal nas ikkl gadgudatkc Kxahpdk? Kxahpdk?  Wupp`sk tnk hkal `b 7 luhikrs fs >.5   Dkt ^1 8 : Dkt ^9 8 > Znat fs  fs ^70

Fb tnk hkal `b tnksk tnrkk vaduks fs >.5, tnkl ^7 hust ik 6 6   (f.k., ^7 fs l`t brkk t` vary)

Nkrk, l 8 7, s` ckjrkks `b brkkc`h 8 l ‗ 1 8 7 ‗ 1 8 9 (9 vaduks gal ik aly luhikrs, iut tnk tnfrc fs l`t brkk t` vary b`r a jfvkl hkal)

Gnap :-35

Wtatfstfgs b`r Iusflkss alc Kg`l`hfgs, 2k © 955: Ukars`l Kcugatf`l, Flg.  

Gnf-squark Kxahpdk 





 A g`hhkrgfad g`hhkrgfad brkkzkr hust n`dc a skdkgtkc tkhpkraturk wftn dfttdk varfatf`l. Wpkgfbfgatf`ls gadd b`r a stalcarc ckvfatf`l `b l` h`rk tnal 3 ckjrkks (a varfalgk `b 12 ckjrkks).

 A sahpdk `b 13 13 brkkzkrs fs t` ik tkstkc Znat fs tnk uppkr dfhft (M) b`r tnk sahpdk varfalgk sugn tnat tnk pr`iaifdfty `b kxgkkcflj tnfs dfhft, jfvkl tnat tnk p`pudatf`l stalcarc ckvfatf`l fs 3, fs dkss tnal 5.5;0

Gnap :-31

Gnap :-39

Wtatfstfgs b`r Iusflkss alc Kg`l`hfgs, 2k © 955: Ukars`l Kcugatf`l, Flg.  

Bflcflj tnk Gnf-squark Raduk 9

 ϊ 

 

(l  1)s 9 χ9

Fs gnf-squark cfstrfiutkc wftn (l ‗ 1) 8 17 ckjrkks `b brkkc`h

[sk tnk tnk gnf-squark cfstrfiutf`l wftn arka 5.5; fl tnk uppkr tafd?  917 8 99.72 (α 8 .5; alc 13 ‗ 1 8 17 c.b.) pr`iaifdfty α 8 .5; 9



 917 8 99.72 Gnap :-37

Wtatfstfgs b`r Iusflkss alc Kg`l`hfgs, 2k © 955: Ukars`l Kcugatf`l, Flg.  

Gnf-squark Kxahpdk (g`ltflukc)  917

W`?

8 99.72  (α 8 .5; alc 13 ‗ 1 8 17 c.b.)  (l  1)s 9 U(s  M)  U       12 9

(l  1)M 12

`r 

s`

M

  ϊ    5.5; 17   9

 99.72

(wnkrk l 8 13)

(99.72)(12 )    9:.;9 (13  1)

Fb s9 br`h tnk sahpdk `b sfzk l 8 13 fs jrkatkr tnal 9:.;9, tnkrk fs str`lj kvfcklgk t` sujjkst tnk p`pudatf`l varfalgk kxgkkcs 12.