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rQ`Q/F r; bFHB T;`X CFQ bvMQMBKm /H i2;Q ivTm xKB2MMv+? mʊvr bBĠ i2`KBMm ivT Fi2;Q`BHMvX CF rB/É x TQ/Mv+? T`xvFƈ/Ʀr- xKB2MM2 i2;Q ivTm M Q;Ʀƈ T`xvDKmD² r`iQȐ+B MB2MmK2`v+xM2  D2ȐHB Mr2i xKB2MMvK ivK M/D2 bBĠ r`iQȐ+B HB+x#Qr2- iQ T2ƈMB² QM2 `QHĠ FQ/Ʀr +xv Mxr Fi2;Q`BB UFHbV B rvFQMvrMB2 M MB+? /xBƈƖ `viK2iv+xMv+? KQʊ2 MB2 KB2É b2MbmX w FQH2B- bTQȐ`Ʀ/ xKB2MMv+? ivTm DFQȐ+BQr2;Q UFi2;Q`BHM2;QV rv`Ʀʊ@

MBKv

UV wKB2MM2 ivTm MQKBMHM2;Q- iDX xKB2MM2- FiƦ`v+? r`iQȐ+B KQʊM x@

FrHB}FQrÉ /Q TQbx+x2;ƦHMv+? UrxD2KMB2 rvFHm+xD²+v+? bBĠV F@

i2;Q`BB- H2 Fi2;Q`BB iv+? MB2 KQʊM r bTQbƦ# Mim`HMv mTQ`x²/FQ@

rÉ UMTX TQT`x2x rbFxMB2 FB2`mMFm rx`Qbim MiĠʊ2MB /M2D +2+?v +?`Fi2`vbiv+xM2DVX S`xvFƈ/v xKB2MMv+? ivTm MQKBMHM2;Q iQ, Tƈ2É T+D2Mi- FQHQ` Q+xm- D2/MQbiF +?Q`Q#Qr- M FiƦ`² +B2`TB T+D2Mi-

;`mTv F`rBX

U#V wKB2MM2 ivTm TQ`x²/FQr2;Q

- iDX xKB2MM2- FiƦ`v+? r`iQȐ+B KQʊM

xFrHB}FQrÉ /Q TQbx+x2;ƦHMv+? UrxD2KMB2 rvFHm+xD²+v+? bBĠV Fi2;Q`BB B Fi2;Q`B2 i2 KD² Mim`HMv TQ`x²/2F UMTX KQʊM rbFxÉ FB2`mM2F rx`Qbim MiĠʊ2MB /M2D +2+?v +?`Fi2`vbiv+xM2D Hm# KQʊM

rbirBÉ xMF MB2`ƦrMQȐ+B TQKBĠ/xv TQbx+x2;ƦHMvKB Fi2;Q`BKBVX S`xvFƈ/v xKB2MMv+? ivTm TQ`x²/FQr2;Q iQ, MiĠʊ2MB2 #ƦHm Q/+xmr@

M2;Q T`x2x T+D2Mi Ubƈ#v- mKB`FQrMv- bBHMvV- biQTB2Ɩ xrMbQ@

rMB +?Q`Q#v UH2FFQ +?Q`v- +BĠʊFQ +?Q`v- #`/xQ +BĠʊFQ +?Q`vV- i2K@

T2`im` +Bƈ UTQMBʊ2D jdê*- TQKBĠ/xv jdê* B jNê*- TQrvʊ2D jNê*VX

NVwmrʊKv- ʊ2 MB2 ivHFQ xKB2MM2 ivTm DFQȐ+BQr2;Q KQ;² #vÉ xKB2MMvKB ivTm TQ`x²/FQ@

r2;Q- TQMB2rʊ xKB2MM2 ivTm BHQȐ+BQr2;Q b² r Mim`HMv bTQbƦ# xrbx2 ivTm TQ`x²/FQr2;Q x TQ`x²/FB2K rvxM+xQMvK T`x2x `2H+DĠ MB2`ƦrMQȐ+B dz≤Ǵ r Fʊ/vK x#BQ`x2 HB+x#QrvKX

_Qx/xBƈ R

ahhuahuE PSAaPq

RXRX _QxFƈ/ +xĠbiQȐ+B B ;`}+xM T`2x2Mi+D /Mv+?

RXRXRX P`;MBx+D /Mv+? r TQbi+B i#2H`v+xM2D

wrvFH2- x2#`M2 ǵbm`Qr2Ƕ /M2 MB2rB2H2 KƦrB² Q BMi2`2bmD²+2D Mb +2bx2 UHm#

+2+?+?V- FiƦ`² +?+2Kv #/É B /QTB2`Q TQ /QFQMMBm Q/TQrB2/MB2;Q T`x2Fbxiƈ@

+2MB iv+? /Mv+? KQʊ2Kv mxvbFÉ x MB+? /mʊQ rBĠ+2D BM7Q`K+DBX

S`xvFƈ/ RXRXRX q xFƈ/xB2 T`+v ey T`+QrMBFQK rv#`M2D ;`mTv xKB2`xQMQ +BȐMB2MB2 iĠiMB+x2 F`rBX qvMBFB TQKB`m +BȐMB2MB iĠiMB+x2;Q bFm`+xQr2;Q UKK >;V xrB2` TQMBʊbx i#2HX

117 136 128 144 120 133 111 121 118 136 124 133 130 119 133 131 127 126 101 108 158 112 114 103 130 119 111 128 130 141 132 124 129 161 116 155 129 109 129 132 140 145 124 152 133 112 132 119

120 102 122 104 117 142 111 127 120 125 114 121 N hFB2 /M2 MxvrM2 b² i2ʊ bx2`2;B2K MB2mTQ`x²/FQrMvKX JQʊM D2 mTQ@

`x²/FQrÉ- MTX rv#B2`D²+ T`x2/xBƈv HB+x#Qr2 iF- #v #vƈv QM2 `Qxƈ²+xM2- `ƦrM2D /ƈm;QȐ+B UH2 +xbKB b² rvD²iFBV B Fʊ/v 2H2K2Mi i2;Q x#BQ`m xMHxƈ bBĠ /QFƈ/MB2 r D2/MvK x iv+? T`x2/xBƈƦrX LbiĠTMB2- HB+xvKv BH2 2H2K2MiƦr Mbx2;Q x#BQ`m x@

rB2` Fʊ/v x iv+? T`x2/xBƈƦr- Qi`xvKmD²+ ixrX `QxFƈ/ +xĠbiQȐ+B- iDX x#BƦ` FHb B Q/TQrB/D²+v+? BK +xĠbiQȐ+BX q TQHbFB2D HBi2`im`x2 `QxFƈ/ +xĠbiQȐ+B M@

xvrMv D2bi bx2`2;B2K `Qx/xB2H+xvK Ur ivK T`xvT/Fm bx2`2;B2K `Qx/xB2H+xvK T`x2/xBƈQrvKV-  +xĠbiQȐ+B MxvrM2 b² i2ʊ HB+x2#MQȐ+BKB Hm# HB+xMQȐ+BKBX

.mʊQ BM7Q`K+DB M TQ/birB2 x2#`Mv+? /Mv+? /D2 MK i2ʊ rx;HĠ/Mv `Qx@

Fƈ/ +xĠbiQȐ+BX Pi`xvKKv ;Q- D2ȐHB +xĠbiQȐ+B r TQbx+x2;ƦHMv+? FHb+? TQ/xB2@

HBKv T`x2x HB+x#Ġ 2H2K2MiƦr r x#BQ`x2 /Mv+?X qx;HĠ/Mv `QxFƈ/ +xĠbiQȐ+B KQʊM

i2ʊ rv`xBÉ r T`Q+2Mi+?- KMQʊ²+ +xĠbiQȐ+B rx;HĠ/M2 T`x2x 100 UTKBĠiDKv- ʊ2 bvK#QH W iQ MB+ BMM2;Q DF 1=100VX qx;HĠ/Mv `QxFƈ/ +xĠbiQȐ+B r T`Q+2Mi+? MB2 D2bi biM/`/QrvK 2H2K2Mi2K i#2HB `QxFƈ/m +xĠbiQȐ+B- H2 +xbKB #Ġ/xB2Kv ;Q mKB2bx+xÉ r i#2HB- TQMB2rʊ rvFQ`xvbimD2 bBĠ ;Q r rvF`2b+? FQƈQrv+?X

h#2H RXR T`x2/birB `QxFƈ/ +xĠbiQȐ+B B `QxFƈ/ +xĠbiQȐ+B rx;HĠ/Mv+? +BȐMB2@

MB iĠiMB+x2;Q bFm`+xQr2;Q TQ//M2D #/MBm ;`mTv x S`xvFƈ/m RXRXRX SQMB2rʊ

T`rv FQMB2+ T`x2/xBƈm FHbQr2;Q Ux rvD²iFB2K QbiiMB2;QV D2bi `ƦrMv H2r2Km

RXRX _QxFƈ/ +xĠbiQȐ+B B ;`}+xM T`2x2Mi+D /Mv+? Rd

FQƖ+QrB T`x2/xBƈm MbiĠTmD²+2;Q TQ MBK- iQ /H xT2rMB2MB `Qxƈ²+xMQȐ+B iv+?

T`x2/xBƈƦr #Ġ/xB2Kv xFƈ/É- ʊ2 D2bi iQ T`x2/xBƈ H2rQbi`QMMB2 /QKFMBĠiv

- iDX H2rv FQMB2+ T`x2/xBƈm FHbQr2;Q D2bi rƈ²+xQMv /Q T`x2/xBƈm-  T`rv MB2X

h#2H RXR _QxFƈ/ +xĠbiQȐ+B B rx;HĠ/Mv `QxFƈ/ +xĠbiQȐ+B +BȐMB2MB iĠiMB+x2;Q F`rB r #/M2D ;`mTB2

EHbv *xĠbiQȐÉ *xĠbiQȐÉ rx;HĠ/M *xĠbiQȐÉ rx;HĠ/M r UWV

100 − 110 6 0;1000 10;00

110 − 120 14 0;2333 23;33

120 − 130 18 0;3000 30;00

130 − 140 13 0;2167 21;67

140 − 150 5 0;0833 8;33

150 − 160 3 0;0500 5;00

160 − 170 1 0;0167 1;67

amK 60 1;0000 100;00

h2`x ƈirQ D2bi- MTX xmrʊvÉ- ʊ2 x/2+v/QrM rBĠFbxQȐÉ T`+QrMBFƦr K

+BȐMB2MB2 r ;`MB++? Q/ 110 /Q 140 KK >;X wmrʊKv- ʊ2 r `QxTi`vrMvK T`xvFƈ/xB2 xKB2MM- FiƦ`² D2bi +BȐMB2MB2 bFm`+xQr2 F`rB- D2bi ivTm BHQȐ+BQr2;QX

S`x2D/ʆKv i2`x /Q T`xvFƈ/m `QxFƈ/m +xĠbiQȐ+B xKB2MM2D ivTm DFQȐ+BQr2;Q UFi2;Q`BHM2;QVX

S`xvFƈ/ RXRXkX qv#`MQ /M2 Ny T+D2MiƦr B rvTBbMQ B+? ;`mTv F`rB r`x x +xvMMBFB2K _? U+ Hm# − T`xv ;`mTB2 F`rBVX .M2 i2 xrB2` TQMBʊbx i#2HX

y+ y+ y− y+ y+ y+ + + + y+ − y−

"+ y+ "+ + + "− "+ y+ "− "+ − y+

y+ "+ y+ y+ y+ y+ "− + + y+ y+ y+

y+ + "+ + y+ + y+ "+ + y− y+ y+

"+ y+ + "+ "− y+ + y+ + + y+ y+

"+ "− y+ + + y+ + "+ y− y+ + y+

y+ "+ y− + + y+ y+ "+ y+ − y+ "−

+ y− + y+ + "+

SQ TQHB+x2MBm +xĠbiQȐ+B Qi`xvKmD2Kv `QxFƈ/ +xĠbiQȐ+B B rx;HĠ/Mv `QxFƈ/ +xĠ@

biQȐ+B Ubx2`2; `Qx/xB2H+xv TmMFiQrvV- FiƦ`2 iQ xTBbHBȐKv r h#2HB RXkX

wmrʊKv- ʊ2 r T`x2+BrB2ƖbirB2 /Q xKB2MM2D ivTm BHQȐ+BQr2;Q- ;/xB2 FHbKB

#vƈv T`x2/xBƈv HB+x#Qr2 xrM2 i2ʊ T`x2/xBƈKB FHbQrvKB- /H xKB2MM2D ivTm DFQȐ+BQr2;Q FHbKB b² rbxvbiFB2 r`iQȐ+B- FiƦ`2 i xKB2MM KQʊ2 T`xvDKQrÉX

RVq rB2Hm TFB2i+? biivbiv+xMv+? D2bi KQʊHBrQȐÉ rv#Q`m H#Q H2rQbi`QMMB2 /QKFMBĠi2;Q T`x2/xBƈm FHbQr2;Q H#Q T`rQbi`QMMB2 /QKFMBĠi2;Q x rv#Q`2K i2;Q /`m;B2;Q DFQ QT+D² /Q@

KvȐHM²X

R3 RX aiivbivF QTBbQr

h#2H RXk

_QxFƈ/ ;`mT F`rB r #/M2D ;`mTB2

EHbv *xĠbiQȐÉ *xĠbiQȐÉ rx;HĠ/M *xĠbiQȐÉ rx;HĠ/M r UWV

y+ 37 0;4111 41;11

y− 6 0;0667 6;67

+ 24 0;2667 26;67

− 3 0;0333 3;33

"+ 12 0;1333 13;33

"− 4 0;0444 4;44

"+ 2 0;0222 2;22

"− 2 0;0222 2;22

amK 90 0;9999

99;99

Vw2 rx;HĠ/m M xQF`²;H2MB /Q +xi2`2+? KB2Db+ TQ T`x2+BMFm bmK rx;HĠ/Mv+? +xĠbiQȐ+B rvMQbB 0;9999-  MB2 1X w TQrQ/m xQF`²;H2Ɩ bmK +xĠbiQȐ+B r T`Q+2Mi+? rvMBQbƈ 99;99W-  MB2 100WX C2ȐHB D2/MF #Ġ/xB2Kv FQ`xvbiÉ x2 biivbiv+xM2;Q T`Q;`Km FQKTmi2`Qr2;Q B D2ȐHB Mr2i rvMBFB #Ġ/² rvȐrB2iHM2- MTX x /rQK KB2Db+KB TQ T`x2+BMFm- iQ Q#HB+x2MB #Ġ/² rvFQMvrM2 D2/MF x /mʊ² rBĠFbx² /QFƈ/MQȐ+B² B Qi`xvKM2 rvMBFB #Ġ/² M Q;Ʀƈ TQT`rM2- iDX iK ;/xB2 KKv Qi`xvKÉ R iQ Qi`xvKKv R-  ;/xB2 RyyW iQ Qi`xvKKv RyyWX N

*xvHB /H iFB2D xKB2MM2D KKv ivH2 FHb BH2 `ƦʊMv+? r`iQȐ+B QM T`xvDKmD2X q MbxvK T`xvFƈ/xB2 FHbKB b² rbxvbiFB2 ;`mTv F`rB x /Q/MvK xMFB2K ǵ+Ƕ B ǵ−Ƕ U+xvMMBF _?VX SQ/F`2ȐHKv xi2K- ʊ2 T`x2/xBƈƦr FHbQrv+? UHB+x#Qrv+?V mʊvrKv /H /Mv+? BHQȐ+BQrv+? ivTm +B²;ƈ2;Q DF B ivTm /vbF`2iM2;QX q ivK QbiiMBK T`xv@

T/Fm ivHFQ ri2/v- ;/v #/M xKB2MM U+2+?V T`xvDKmD2 rB2H2 `ƦʊMv+?

r`iQȐ+B UMTX TQM/ 20 +?QÉ MB2 KKv imiD DFB2DȐ bxivrM2D `2;mƈvVX LiQKBbi

;/v /M2 `2T`2x2MimD² xKB2MM² ivTm DFQȐ+BQr2;Q- iQ FHbKB b² rbxvbiFB2 T`xvD@

KQrM2 T`x2x iĠ xKB2MM² r`iQȐ+BX

q T`xvT/Fm `QxFƈ/m +xĠbiQȐ+B x T`x2/xBƈKB FHbQrvKB H2rv FQMB2+ T`x2@

/xBƈm MxvrKv /QHM² ;`MB+² T`x2/xBƈm FHbQr2;Q-  T`rv FQMB2+ T`x2/xBƈm

;Ʀ`M² ;`MB+² T`x2/xBƈm FHbQr2;QX _ƦʊMB+Ġ KBĠ/xv ;Ʀ`M² B /QHM² ;`MB+² T`x2@

/xBƈm FHbQr2;Q MxvrKv bx2`QFQȐ+B² Hm# `QxTBĠiQȐ+B² T`x2/xBƈm FHbQr2;QX SQ/bmKmDKv r TmMFi+? T`Q+2b irQ`x2MB i#2HB `QxFƈ/m +xĠbiQȐ+BX

RX qvxM+xKv r`iQȐÉ MDrBĠFbx² B MDKMB2Dbx² r x#BQ`x2 /Mv+?- D2ȐHB KKv /Q +xvMB2MB x /MvKB ivTm BHQȐ+BQr2;Q B Q#HB+xKv `QxbiĠT r MHBxQr@

MvK x#BQ`x2 /Mv+?- iDX `ƦʊMB+Ġ TQKBĠ/xv xMH2xBQM² r`iQȐ+B² MDrBĠFbx² B MDKMB2Dbx²- #v rvxM+xvÉ T`x2/xBƈ HB+x#Qrv- FiƦ`v MH2ʊv TQ/xB2HBÉ M

FHbvX *xĠbiQ i2M T`x2/xBƈ HB+x#Qrv `Qxbx2`x bBĠ MB2+Q- #BQ`²+ DFQ H2rv FQMB2+ i2;Q T`x2/xBƈm ǵrv;Q/M²Ƕ /H Mb HB+x#Ġ M H2rQ Q/ r`iQȐ+B MD@

KMB2Dbx2D r x#BQ`x2 /Mv+?-  DFQ T`rv FQMB2+ i2;Q T`x2/xBƈm ǵrv;Q/M²Ƕ

/H Mb HB+x#Ġ M T`rQ Q/ r`iQȐ+B MDrBĠFbx2D r x#BQ`x2 /Mv+?X

RXRX _QxFƈ/ +xĠbiQȐ+B B ;`}+xM T`2x2Mi+D /Mv+? RN

kX qvxM+xKv HB+x#Ġ FHb- D2ȐHB KKv /Q +xvMB2MB x /MvKB ivTm BHQȐ+BQr2;QX SQrbx2+?MB2 mrʊ bBĠ- ʊ2 T`xv FQMbi`mF+DB `QxFƈ/m +xĠbiQȐ+B HB+x# T`x2@

/xBƈƦr FHbQrv+? TQrBMM rvMQbBÉ Q/ 5 /Q 20X A +?QÉ MB2 K im bxivrM2D

`2;mƈv- iQ #`/xQ rʊMvK D2bi mirQ`x2MB2 rvbi`+xD²+Q /mʊQ FHb- #v /Q@

#`x2 QTBbÉ /M2X C2ȐHB x#BƦ` /Mv+? xrB2` n 2H2K2MiƦr- iQ `Qxb²/MvK D2bi rv#B2`MB2 HB+x#v T`x2/xBƈƦr FHbQrv+? k- FB2`mD²+ bBĠ D2/M² x TQMBʊbxv+?

`2FQK2M/+DB,

UV HB+x# FHb k r T`xv#HBʊ2MBm `ƦrM √n- U#V HB+x# FHb k `ƦrM +xĠȐ+B +ƈFQrBi2D 5 ln n-

U+V HB+x# FHb k `ƦrM +xĠȐ+B +ƈFQrBi2D 1 + 3;322 ln nX

#v FHbv #vƈv `Qxƈ²+xM2 MH2ʊv x/2+v/QrÉ- +xv T`x2/xBƈv FHbQr2 KD²

#vÉ TƦƈ/QKFMBĠi2 x H2r2D +xv x T`r2DX Pi`xvKM2 T`x2/xBƈv FHbQr2 rTB@

bmD2Kv r TB2`rbx2D FQHmKMB2 i#2HBX

jX LbiĠTMB2- HB+xvKv BH2 r`iQȐ+B U/Mv+?V xMD/mD2 bBĠ r TQbx+x2;ƦHM2D FHbB2 B mxvbFM2 HB+x#v MxvrM2 +xĠbiQȐ+BKB UHm# HB+x2#MQȐ+BKB FHbV rTBbmD2Kv r /`m;B2D FQHmKMB2 i#2HB M rvbQFQȐ+B Q/TQrB/D²+v+? BK FHbX

9X .xB2H²+ Qi`xvKM2 r TQT`x2/MBK F`QFm +xĠbiQȐ+B T`x2x HB+x#Ġ rbxvbiFB+?

/Mv+?- Qi`xvKmD2Kv +xĠbiQȐ+B rx;HĠ/M2- FiƦ`2 xTBbmD2Kv r i`x2+B2D FQ@

HmKMB2X

8X *xĠbiQ T`xv/iMvK D2bi rv`ʊ2MB2 +xĠbiQȐ+B rx;HĠ/M2D r T`Q+2Mi+? B xTB@

bMB2 D2D r +xr`i2D FQHmKMB2X Pi`xvKmD2 bBĠ D² x i`x2+B2D FQHmKMv- KMQʊ²+

rvbiĠTmD²+2 r MB2D HB+x#v T`x2x 100X w +xĠbiQȐ+B rx;HĠ/M2D r T`Q+2Mi+?

FQ`xvbiKv- irQ`x²+ M T`xvFƈ/ rvF`2b FQƈQrv /H `QxFƈ/m +xĠbiQȐ+B

X

*xbKB T`xv/iMvK D2bi mʊv+B2 ixrX `QxFƈ/m bFmKmHQrMv+? +xĠbiQȐ+B- FiƦ`v TQFxmD2 +xĠbiQȐ+B MB2 r /M2D FHbB2- H2 r T`x2/xBƈ+? QF`2ȐHQMv+? MB2`ƦrMQȐ+B² dzKMB2Dbxv Hm# `ƦrM2Ǵ /M2D HB+x#B2- xrvFH2 `ƦrM2D ;Ʀ`M2D ;`MB+v TQbx+x2;ƦHM2;Q T`x2/xBƈm FHbQr2;QX lxvbFmD2 bBĠ ;Q- bmKmD²+ FQH2DM2 +xĠbiQȐ+B r FHb+?X LTX r S`xvFƈ/xB2 RXRXR bFmKmHQrM +xĠbiQȐÉ /H TB2`rbx2D FHbv rvMQbB 0 + 6 = 6- /H

/`m;B2D FHbv D2bi `ƦrM 0 + 6 + 14 = 20- /H i`x2+B2D 0 + 6 + 14 + 18 = 38 Bi/X .H

/`m;B2D- i`x2+B2D B /Hbxv+? FHb bFmKmHQrM2 +xĠbiQȐ+B KQʊM i2ʊ mxvbFÉ- /Q/@

D²+ /Q TQT`x2/MB2D bFmKmHQrM2D +xĠbiQȐ+B +xĠbiQȐÉ /H /M2D FHbvX q TQ/MvK T`xvFƈ/xB2- bFmKmHQrM2 +xĠbiQȐ+B 20- 38 KQʊM mxvbFÉ- rvFQMmD²+ Q#HB+x2MB

6 + 14 = 20 - 20 + 18 = 38 Bi/X q TQ/Q#Mv bTQbƦ# irQ`xvKv `QxFƈ/ bFmKm@

HQrMv+? +xĠbiQȐ+B rx;HĠ/Mv+? B `QxFƈ/ bFmKmHQrMv+? +xĠbiQȐ+B r T`Q+2Mi+?X

kVhrQ`x2MB2 rvF`2bm FQƈQr2;Q K b2Mb- D2ȐHB HB+x# FHb MB2 D2bi x#vi /mʊX q T`x2+BrMvK

`xB2- bx+x2;ƦHMB2 r +x`MQ@#BƈvK /`mFm- KQʊ2Kv Qi`xvKÉ x#vi Kƈ2 B KƈQ Q/`ƦʊMBHM2 Q/

bB2#B2 rv+BMFB FQƈ- TQrQ/mD²+2 Kƈ² +xvi2HMQȐÉ rvF`2bmX

ky RX aiivbivF QTBbQr

qvbi`+xv xKBbi +xĠbiQȐ+B mʊvÉ Q/TQrB2/MBQ +xĠbiQȐ+B rx;HĠ/Mv+? B +xĠbiQȐ+B rx;HĠ/Mv+? r T`Q+2Mi+?X

S`xvFƈ/ RXRXjX :`mTB2 60 T+D2MiƦr x i2KT2`im`² +Bƈ jNê* B rvʊbx² TQ/MQ H2F-  MbiĠTMB2 +Q ;Q/xBMĠ KB2`xQMQ i2KT2`im`Ġ- #v bT`r/xBÉ TQ BHm ;Q/xBM+?

i2KT2`im` +Bƈ Q#MBʊvƈ bBĠ Q +Q MDKMB2D Rê*X lxvbFM2 /M2 xrB2` TQMBʊbx

i#2HX

3 3 4 4 3 3 4 2 3 2 2 3 3 3 1 4 3 1 3 1

3 2 2 4 3 5 3 3 2 3 2 4 1 4 5 5 3 3 6 2

3 3 1 2 2 2 1 4 5 5 1 2 4 2 3 5 4 4 3 4

SQMB2rʊ `QxbiĠT r ivK x#BQ`x2 /Mv+? D2bi Kƈv U6 − 1 = 5V- iQ FHbKB

#Ġ/² im TQD2/vM+x2 r`iQȐ+B /Mv+?- iDX HB+x#v 1; 2; 3; 4; 5; 6X w2 rx;HĠ/m M iQ- ʊ2 KB2`xQMv +xb D2bi xKB2MM² ivTm +B²;ƈ2;Q xrvFH2 irQ`xv bBĠ T`x2/xBƈv FHbQr2 Q /ƈm;QȐ+B 1- Q/2DKmD²+ Q/ HB+x# #Ġ/²+v+? FHbKB 0;5 B /Q/D²+ /Q MB+? 0;5 Ur ivK T`xvT/Fm FHbv B T`x2/xBƈv FHbQr2 MB2 #Ġ/² iQʊbK2- DF #vƈQ iQ r+x2ȐMB2DVX SQbiĠTmD²+ iF- Qi`xvKKv MbiĠTmD²+² i#2HĠ `QxFƈ/m +xĠbiQȐ+B

h#2H RXj

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aFmKmHQrM

EHbv S`x2/xBƈv *xĠbiQȐÉ aFmKmHQrM *xĠbiQȐÉ +xĠbiQȐÉ *xĠbiQȐÉ

FHbQr2 +xĠbiQȐÉ rx;HĠ/M rx;HĠ/M rx;HXUWV

1 0;5 − 1;5 7 7 0;1167 0;1167 11;67

2 1;5 − 2;5 13 20 0;2167 0;3334 21; 67

3 2;5 − 3;5 21 41 0;3500 0;6834 35;00

4 3;5 − 4;5 12 53 0;2000 0;8834 20;00

5 4;5 − 5;5 6 59 0;1000 0;9834 10;00

6 5;5 − 6;5 1 60 0;0167 1;0001 1;67

amK 60 1;0001

100;01

#VwQ#X mr;B r T`xvTBbB2 V TQ/ h#2H² RXk M bi`X R3X N

RXRXkX S`xvFƈ/v ;`}+xM2D T`2x2Mi+DB /Mv+?

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Mv+?- rx;HĠ/Mv+? +xv i2ʊ rx;HĠ/Mv+? r T`Q+2Mi+? UMB2bFmKmHQrMv+? B bFmKm@

HQrMv+?V- MDT`QbibxvK B MD+xĠbibxvK bTQbQ#2K B+? ;`}+xM2D T`2x2Mi+DB D2bi

RXRX _QxFƈ/ +xĠbiQȐ+B B ;`}+xM T`2x2Mi+D /Mv+? kR

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Ȑ+B UHB+x2#MQȐ+BV 2H2K2MiƦr MH2ʊ²+v+? /Q /Mv+? T`x2/xBƈƦr FHbQrv+?X _vbX RXR T`x2/birB ?BbiQ;`K `QxFƈ/m +xĠbiQȐ+B +BȐMB2MB iĠiMB+x2;Q bFm`+xQr2;Q mxv@

bFMv M TQ/birB2 FQHmKMv R B k h#2HB RXR-  _vbX RXk T`x2/birB ?BbiQ;`K

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rQȐÉ rT`Qr/x2MB /Q/iFQrv+? 2H2K2MiƦr /Q ?BbiQ;`Km- MTX /Q ?BbiQ;`Km M

_vbX RXR /Q/MQ ixrX F`xvr² `QxFƈ/m MQ`KHM2;Q

MDH2TB2D /QTbQrM² /Q M@

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kk RX aiivbivF QTBbQr

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TQrBMM

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;`mTB2 QbƦ#X

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rMv+?X S`xvFƈ/ iFB2;Q ?BbiQ;`Km /Mv D2bi M _vbX RX8X

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X S`xvFƈ/

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qB2HQ#QF

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RXRX _QxFƈ/ +xĠbiQȐ+B B ;`}+xM T`2x2Mi+D /Mv+? kj

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T`x2/xBƈƦr FHbQrv+?

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rMvKB #Ġ/xB2Kv KƦrBÉ Q/TQrB2/MBQ, Q rB2HQ#QFm +xĠbiQȐ+B- rB2HQ#QFm +xĠbiQȐ+B

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k9 RX aiivbivF QTBbQr

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rx;HĠ/Mv+? B rB2HQ#QFm +xĠbiQȐ+B bFmKmHQrMv+?

X L QbB TQxBQK2D x xb/v x@

xM+xKv D2bx+x2 D2/M² r`iQȐÉ M H2rQ Q/ Ȑ`Q/F TB2`rbx2;Q T`x2/xBƈm +xĠbiQȐ+B UM _vbX RXd D2bi MB² r`iQȐÉ N8V r iFB bTQbƦ#- #v Q/H2;ƈQȐ+B rbxvbiFB+? b²@

3VLxvrMvK i2ʊ F`xvr² rx`Qbim +xĠbiQȐ+B-  r DĠxvFm M;B2HbFBK Q;Bp2X lr;, .H /Mv+?

ivTm +B²;ƈ2;Q xKBbi Ȑ`Q/FƦr T`x2/xBƈƦr FHbQrv+? ƈ²+xvKv FQƖ+2 iv+? T`x2/xBƈƦrX

RXkX PTBb biivbiv+xMv k8

bB2/MB+? xxM+xQMv+? rbTƦƈ`xĠ/Mv+? #vƈv D2/MFQr2-  r T`xvT/Fm rB2HQ#QFm +xĠbiQȐ+B B +xĠbiQȐ+B rx;HĠ/Mv+? xxM+xKv r TQ/Q#Mv bTQbƦ# D2bx+x2 /`m;² r`iQȐÉ M T`rQ Q/ Ȑ`Q/F QbiiMB2;Q T`x2/xBƈm +xĠbiQȐ+B UM _vbX RXd D2bi MB² r`iQȐÉ Rd8VX hvK /Q/MvK rbTƦƈ`xĠ/MvK T`xvTBbmD2Kv x2`Qr2 +xĠbiQȐ+BX qB2@

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_vbX RXdX qB2HQ#QF +xĠbiQȐ+B /H +BȐMB2MB iĠiMB+x2;Q bFm`+xQr2;Q

_vbX RXd T`x2/birB rvF`2b rB2HQ#QFm +xĠbiQȐ+B /H +BȐMB2MB iĠiMB+x2;Q bFm`@

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i2KT2`im`v +Bƈ Q +Q MDKMB2D Rê* /H /Mv+? x h#2HB RXjX

RXkX PTBb biivbiv+xMv

RXkXRX JB`v i2M/2M+DB +2Mi`HM2D

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ke RX aiivbivF QTBbQr

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rvFQ`xvbimD²+ +ƈ² TQTmH+DĠX .2}MB+D2 MB2FiƦ`v+? TQDĠÉ- FiƦ`2 rT`Qr/xBKv r

i2D b2F+DB KQ;² bBĠ `ƦʊMBÉ r xH2ʊMQȐ+B Q/ i2;Q +xv #Ġ/² bBĠ QM2 Q/MQbBÉ /Q T`Ʀ#v

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RXkX PTBb biivbiv+xMv kd

2H2K2MiƦr r TQTmH+DB HBi2`² NX

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U+B²;ƈ2;Q B /vbF`2i@

M2;QVc

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FB+? r`iQȐ+B 2H2K2MiƦr i2;Q x#BQ`m TQ/xB2HQM T`x2x HB+x#Ġ D2;Q 2H2K2MiƦrX ȏ`2/@

MB² /H T`Ʀ#v x

; : : : ; x

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; : : : ; x

QxM+xvKv ;`2+F² HBi2`² —X JKv rQ#2+ i2;Q MbiĠTmD²+2 rxQ`v,

ȏ`2/MB /H T`Ʀ#v, x = x

+ x

+ · · · + x

n ; URXRV

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+ x

+ · · · + x

N : URXkV

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rMB ^P U;`2+F /mʊ HBi2` bB;KV

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x = 1 n

n

X

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N

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x

: URXjV

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x

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; x

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/mD2- Q/ /rƦ+? b²bB2/MB+? HBMBD2F i2Fbim D2bi xM+xMB2 rBĠFbxv MBʊ Q/biĠTv TQKBĠ/xv TQxQbiƈvKB HBMBDFKB i2FbimX

k3 RX aiivbivF QTBbQr

S`xvFƈ/ RXkXRX SQMBʊbx i#2H xrB2` r;B MQrQ`Q/FƦr Ur F;V m`Q/xQMv+? r rv#`MvK iv;Q/MBm r T2rMvK bxTBiHmX P#HB+xvÉ Ȑ`2/MB² r;Ġ MQrQ`Q/FX

9-yN j-dN j-e3 j-83 9-y8 j-eN k-38 j-R3 j-9R j-dR j-de j-RR j-NR j-3y k-Nd k-Ne k-dy 9-yR j-dk k-Nd _QxrB²xMB2,

P

i=1

x

= 4;09 + 3;79 + 3;68 + 3;58 + 4;05 + 3;69 + 2;85 + 3;18 + 3;41 + 3;71 + 3;76 + 3;11 + 3;91 + 3;80 + 2;97 + 2;96

+ 2;70 + 4;01 + 3;72 + 2;97 = 69;94:

wi2K x =

P

i=1

x

20 = 69;94

20 = 3;497:

N

*xĠbiQ ;`MB+2 bmKQrMB i = 1 B n r2 rxQ`x2 ^P

x

QTmbx+x bBĠ- D2ȐHB xKB2MM K ivHFQ D2/2M

BM/2Fb- MTX i- B TBbx2 bBĠ ri2/v ^P x

- +Q QxM+x- ʊ2 MH2ʊv xbmKQrÉ r`iQȐ+B x

/H rbxvbiFB+? iX

lr; RXkXRX C2/M² x ;ƈƦrMv+? r/ Ȑ`2/MB2D D2bi D2D r`ʊHBrQȐÉ M Fʊ/² r`iQȐÉ bFƈ/MBF bmKv Q#HB+xM2D TQ/+xb D2D rvxM+xMB- iF ʊ2 TQD2/vM+x r`iQȐÉ /@

M2D KQ+MQ `ƦʊMB²+ bBĠ Q/ r`iQȐ+B TQxQbiƈv+? /Mv+?

KQʊ2 xM+xMB2 xKB2MBÉ r`iQȐÉ Ȑ`2/MB2DX

lr; RXkXkX P#HB+xMB2 Ȑ`2/MB+?- +?QÉ ƈir2 /Q rvFQMMB FQ`xvbiD²+ Mr2i x T`Qbi2;Q FHFmHiQ`- MD+xĠȐ+B2D #Ġ/xB2 rvFQMvrM2 T`x2x T`Q;`Kv biivbiv+xM2 DFQ D2/2M x 2H2K2MiƦr rȐ`Ʀ/ BMMv+? Q#HB+x2Ɩ biivbiv+xMv+?X H2 rB2H2 T`Q;`KƦr biivbiv+xMv+? /D2 MK KQʊHBrQȐÉ Q#HB+xvÉ D² Q//xB2HMB2X

q/v Ȑ`2/MB2D MB2 K KB` i2M/2M+DB +2Mi`HM2D xrM K2/BM²X lTQ`x²/@

FmDKv MB2KH2D²+Q- iDX Q/ MDKMB2Dbx2D /Q MDrBĠFbx2D- /M2 x

; : : : ; x

B iF mTQ@

`x²/FQrMv x#Ʀ` QxM+xvKv DFQ x#BƦ` x

; : : : ; x

X L T`xvFƈ/- /H x#BQ`m 3; 7; 1- ;/xB2 x

= 3- x

= 7 B x

= 1- TQ mTQ`x²/FQrMBm Qi`xvKKv x#BƦ`

1; 3; 7- ;/xB2 x

= 1- x

= 3- x

= 7X

.2}MB+D RXkXkX q x#BQ`x2 /Mv+? `2T`2x2MimD²+v+? r`iQȐ+B T2rM2D xKB2MM2D B #Ġ/²+v+? T`Ʀ#² K2/BM D2bi r`iQȐ+B² Ȑ`Q/FQr² mTQ`x²/FQrM2;Q MB2KH2@

D²+Q Hm# MB2`QbM²+Q rvDȐ+BQr2;Q x#BQ`m /Mv+?X wi2K- ;/v r`iQȐ+B x

; : : : ; x

RjVwKB2MM2 KQ;² KB2É rBĠ+2D BM/2FbƦr- MTX xi j K /r BM/2Fbv i B jX PTmbx+xD²+ D2- MB2 rB2/xB2HB#vȐKv +xv KKv bmKQrÉ TQ Q#m BM/2Fb+? i B j +xv ivHFQ TQ D2/MvK x MB+?X

R9VhFB2 /M2 MxvrKv /MvKB dzQ/biD²+vKBǴ UTQ M;B2HbFm QmiHB2`bVX

RXkX PTBb biivbiv+xMv kN

xKB2MM2D r T`Ʀ#B2 irQ`x² TQ mTQ`x²/FQrMBm +B²; MB2KH2D²+v x

; : : : ; x

- iQ K2/BMĠ x T`Ʀ#v- QxM+xM² bvK#QH2K m

- /2}MBmD2 rxƦ`

m

= 8

> <

> :

x

;/v n D2bi MB2T`xvbi2-

1 2

“ x

+ x

^” ;/v n D2bi T`xvbi2X URX9V SQ/Q#MB2 /2}MBmD2Kv K2/BMĠ TQTmH+DB M

X wKB2MBD²+ r2 rxQ`x2 URX9V m

M M

B Kƈ2 n M /mʊ2 N- Qi`xvKmD2Kv

M

= 8

> <

> :

x

;/v N D2bi MB2T`xvbi2-

1 2

“ x

+ x

^” ;/v N D2bi T`xvbi2X URX8V S`xvFƈ/ RXkXkX qvxM+xKv K2/BMĠ r x#BQ`x2 /Mv+? x S`xvFƈ/m RXkXRX _QxrB²xMB2,

SQ mTQ`x²/FQrMBm /Mv+? MB2KH2D²+Q Qi`xvKKv,

k-dy k-38 k-Ne k-Nd k-Nd j-RR j-R3 j-9R j-83 j-e3 j-eN j-dR j-dk j-de j-dN j-3y j-NR 9-yR 9-y8 9-yN

SQMB2rʊ HB+x# 2H2K2MiƦr Mbx2;Q x#BQ`m D2bi T`xvbi Un = 20V- iQ x

= x

= 3;68  x

= x

= 3;69 UQ#B2 r`iQȐ+B r TQrvʊbx2D i#2HB xxM+xvHBȐKv- xTBbmD²+ D2 iƈmbivK /`mFB2KV B x /`m;B2D HBMBDFB rxQ`m Qi`xvKmD2Kv

m

= 1

2 (3;68 + 3;69) = 3;685X

N S`xvFƈ/ RXkXjX LB2+? MbiĠTmD²+2 /M2

3; 5; 4; 6; 15; 4; 3

rv`ʊD² HB+x#Ġ TQrʊMv+? x#B2;Ʀr +?B`m`;B+xMv+? TQ m`x+? bTQrQ/QrMv+?

rvT/FKB r FQH2DMv+? /MB+? D2/M2;Q x iv;Q/MB Hmi2;QX qvxM+xvÉ Ȑ`2/MB² HB+x#Ġ x#B2;Ʀr +?B`m`;B+xMv+? M D2/2M /xB2Ɩ Q`x K2/BMĠ /H iv+? /Mv+?X

_QxrB²xMB2,

SQ mTQ`x²/FQrMBm

UMB2KH2D²+QV Mbx2;Q x#BQ`m /Mv+? Qi`xvKKv j- j- 9- 9- 8- e- R8

qvFQMmD²+ Q#HB+x2MB- Qi`xvKmD2Kv

R8Vwr`ƦÉKv mr;Ġ M iQ- ʊ2 Ȑ`2/MB MB2 xH2ʊv Q/ FQH2DMQȐ+B r DFB2D rvbiĠTmD² /M2X

jy RX aiivbivF QTBbQr

x = 3 + 3 + 4 + 4 + 5 + 6 + 15

7 = 5;71- m

= x

= 4X

CF rB/xBKv- Q#B2 i2 KB`v i2M/2M+DB +2Mi`HM2D xM+xMB2 bBĠ `ƦʊMB²X L Ȑ`2/MB²- r Q/`ƦʊMB2MBm Q/ K2/BMv- /mʊv rTƈvr K HB+x# 15- xM+xMB2 Q/biD²+ Q/ TQ@

xQbiƈv+? /Mv+?X C2ȐHB T`xv+xvM² i2D /mʊ2D HB+x#v BMi2`r2M+DB +?B`m`;B+xMv+? r TQ`ƦrMMBm /Q `2bxiv /MB iv;Q/MB #vƈQ r ivK /MBm- MTX M;ƈ2 Q#HQ/x2MB2 D2x/MB B +?Q/MBFƦr- iQ K2/BM T2rMB2 H2TB2D MBʊ Ȑ`2/MB T`xv#HBʊ Ȑ`2/MB² /xB2MM² HB+x#Ġ BMi2`r2M+DB r BMMv+? iv;Q/MB+? xBKQrv+? B MB2 xKB2MB bBĠ- D2ȐHB r `QxrʊMv+?

/Mv+? xKBbi 15 xMD/xB2 bBĠ /QrQHM BMM HB+x# rBĠFbx Q/ 3X LiQKBbi Ȑ`2/@

MB- xH2ʊ²+ Q/ r`iQȐ+B Fʊ/2D Q#b2`r+DB- TQxrH MK xmrʊvÉ iFB2 xKBMv

r /Mv+? B xr`Ʀ+BÉ M MB2 mr;ĠX N

h`x2+B KB` i2M/2M+DB +2Mi`HM2D- iDX KQ/ MxvrM i2ʊ /QKBMMi²- D2bi

`x/xB2D mʊvrM MBʊ /rB2 TQT`x2/MB2X

.2}MB+D RXkXjX .H x#BQ`m /Mv+? `2T`2x2MimD²+v+? r`iQȐ+B T2rM2D xKB2MM2D U+2+?vV KQ/² MxvrKv r`iQȐÉ- FiƦ` rvbiĠTmD2 r ivK x#BQ`x2 MD+xĠȐ+B2DX

LB2+? x#BƦ` /Mv+? UQ#b2`r+DBV `2T`2x2MimD2 r`iQȐ+B T2rM2D xKB2MM2DX Ç C2ȐHB r x#BQ`x2 ivK ivHFQ D2/2M 2H2K2Mi rvbiĠTmD2 x MDrBĠFbx² +xĠbiQȐ+B²-

iQ KƦrBKv ri2/v- ʊ2 xKB2MM K `QxFƈ/ D2/MQKQ/HMvX

Ç C2ȐHB r x#BQ`x2 ivK /r 2H2K2Miv rvbiĠTmD² x i² bK² MDrBĠFbx² +xĠbiQȐ+B²- iQ Q# b² KQ/KB B KƦrBKv ri2/v- ʊ2 xKB2MM K `QxFƈ/ /rmKQ/HMv Hm# #BKQ/HMvX

Ç C2ȐHB r x#BQ`x2 ivK rBĠ+2D MBʊ /r 2H2K2Miv rvbiĠTmD² x i² bK² MDrBĠFbx² +xĠbiQȐ+B²- iQ QM2 rbxvbiFB2 b² KQ/KB B KƦrBKv ri2/v- ʊ2 xKB2MM K

`QxFƈ/ rB2HQKQ/HMvX

Ç C2ȐHB r x#BQ`x2 ivK rbxvbiFB2 2H2K2Miv rvbiĠTmD² ivHFQ `x- iQ /H i2;Q x#BQ`m KQ/ MB2 BbiMB2D2X

Si`x²+ M h#2HĠ RXj- rB/xBKv- ʊ2 r S`xvFƈ/xB2 RXRXj KQ/² D2bi HB+x# 3

;Q/xBM- TQMB2rʊ i HB+x# ;Q/xBM rvbiĠTmD2 MD+xĠȐ+B2D r #/MvK x#BQ`x2 B D2D +xĠbiQȐÉ rvbiĠTQrMB rvMQbB 21X .H x#BQ`m /Mv+? x S`xvFƈ/m RXkXR KQ/² D2bi +BĠʊ` MQrQ`Q/F `ƦrMv 2;97 F;X .H x#BQ`m /Mv+? x S`xvFƈ/m RXkXj KQ/KB b² HB+x# 3 B HB+x# 4 BMi2`r2M+DB +?B`m`;B+xMv+? r +B²;m /MBX .H x#BQ`m /Mv+? x S`xvFƈ/m RXRXk Uh#2H RXkV KQ/² D2bi ;`mT F`rB 0+X

RXkXkX Ebxiƈi `QxFƈ/m +xĠbiQȐ+B

_QxFƈ/ +xĠbiQȐ+B KQʊ2 T`xvDKQrÉ `ƦʊM2 FbxiƈivX qv`ƦʊMB bBĠ i`xv Fbxiƈiv

`QxFƈ/m, bvK2i`v+xMv- bvK2i`v+xMv T`rQbi`QMMB2 xrMv i2ʊ bvK2i`v+xMvK

RXkX PTBb biivbiv+xMv jR

T`rQbFQȐMB2 Hm# bvK2i`v+xMvK /Q/iMBQ B bvK2i`v+xMv H2rQbi`QMMB2 xrMv i2ʊ bvK2i`v+xMvK H2rQbFQȐMB2 Hm# bvK2i`v+xMvK mD2KMB2X P /rƦ+? QbiiMB+?

ivT+? `QxFƈ/Ʀr KƦrBKv- ʊ2 b² bFQȐM2X S`xvFƈ/Qr2 rvF`2bv U?BbiQ;`KvV `Qx@

Fƈ/m bvK2i`v+xM2;Q- bvK2i`v+xM2;Q T`rQbi`QMMB2 B bvK2i`v+xM2;Q H2rQbi`QM@

MB2 TQFxM2 b² M _vbX RXRyX C2ȐHB xKB2MM K `QxFƈ/ KQ+MQ bvK2i`v+xMv

.M2 UV, ȏ`2/MB44;23 J2/BM44;50 JQ/45;00 .M2 U"V, ȏ`2/MB42;80

J2/BM42;50 JQ/42;00 .M2 U*V, ȏ`2/MB43;00

J2/BM43;00 JQ/43;00

_vbX RXRyX hvTv `QxFƈ/Ʀr +xĠbiQȐ+B Urv`ƦʊMBHBȐKv TQƈQʊ2MB2 Ȑ`2/MB2D- K2/BMv B KQ/v

`ƦʊMvK ivT2K HBMBB- T`Qr/x²+ D2 Q/ ;Ʀ`M2D F`rĠ/xB Q/TQrB2/MB2;Q bƈmTF UT`QbiQ@

F²iV /Q TmMFim rbFxmD²+2;Q /Mv T`K2i` M QbB TQxBQK2DV

T`rQbi`QMMB2 UDF KB2`xvÉ bFQȐMQȐÉ `QxFƈ/m TQrB2Kv TƦʆMB2DV- iQ rBĠFbxQȐÉ D2D r`iQȐ+B rT/ /Q T`x2/xBƈm M H2rQ Q/ Ȑ`2/MB2D B bFmTB bBĠ r H2rvK FQƖ+m

`QxFƈ/m-  D2;Q ixrX Q;QM xMD/mD2 bBĠ TQ T`r2D bi`QMB2 rvF`2bmX SQM/iQ- D2D Ȑ`2/MB B K2/BM b² M T`rQ Q/ KQ/v Q`x xrvFH2 Ȑ`2/MB D2bi i2ʊ M T`rQ Q/

K2/BMv

X

LiQKBbi- D2ȐHB xKB2MM K `QxFƈ/ KQ+MQ bvK2i`v+xMv H2rQbi`QMMB2- iQ

ReV.H `QxFƈ/Ʀr bvK2i`v+xMv+? T`rQbi`QMMB2 KQʊM D2/MF TQ/É T`xvFƈ/v- /H FiƦ`v+?

Ȑ`2/MB D2bi M H2rQ Q/ K2/BMv-  /H bvK2i`v+xMv+? H2rQbi`QMMB2 M T`rQ Q/ K2/BMvX

jk RX aiivbivF QTBbQr

rBĠFbxQȐÉ D2D r`iQȐ+B rT/ /Q T`x2/xBƈm M T`rQ Q/ Ȑ`2/MB2D B bFmTB bBĠ r T`rvK FQƖ+m `QxFƈ/m-  D2;Q Q;QM xMD/mD2 bBĠ TQ H2r2D bi`QMB2 rvF`2bmX SQM/iQ- D2D Ȑ`2/MB B K2/BM b² M H2rQ Q/ KQ/v Q`x xrvFH2 Ȑ`2/MB D2bi i2ʊ M H2rQ Q/ K2/BMvX

.Hi2;Q r T`xvT/F+? KQ+M2D bvK2i`BB #`/xB2D Q/TQrB2/MB² KB`² i2M/2M+DB +2Mi`HM2D #Ġ/xB2 `+x2D K2/BM MBʊ Ȑ`2/MBX

RXkXjX JB`v xKB2MMQȐ+B U`QxT`Qbx2MB- /vbT2`bDBV w+xMBDKv Q/ MbiĠTmD²+2;Q T`xvFƈ/mX

S`xvFƈ/ RXkX9X qB2`bx  TQMBʊbx2D i#2HB xrB2` mTQ`x²/FQrM2 `QbM²+Q +xbv Q+x2FBrMB Ur /MB+?V rv#`Mv+? R8 T+D2MiƦr M x#B2; r bxTBiHm r D2/M2D KB2Db+QrQȐ+B-  rB2`bx " iF bKQ mTQ`x²/FQrM2 +xbv Q+x2FBrMB rv#`Mv+?

R8 T+D2MiƦr M x#B2; r bxTBiHm r BMM2D KB2Db+QrQȐ+BX qvxM+xvÉ Ȑ`2/MB² B K2@

/BMĠ /H +xbƦr r rB2`bxm  B +xbƦr r rB2`bxm "X

, j e N Rk Rd ky k8 jy jk j8 jN 9y 9R 98 8e

", Rj Rj R9 R8 ky kR ke jy jR j9 je jd j3 9y 9k _QxrB²xMB2,

P#HB+x2MB b² ƈir2 B TQ B+? rvFQMMBm Qi`xvKmD2Kv

x

= x

= 27

- m

= m

= 30: N S`xvFƈ/ i2M TQFxmD2- ʊ2 +?QÉ Ȑ`2/MB2 B K2/BMv /H Q#m x#BQ`Ʀr /Mv+? b² iFB2 bK2- iQ r`iQȐ+B /Mv+? r x#BQ`x2  b² #`/xB2D `QxT`QbxQM2 MBʊ r x#BQ`x2 "X .Hi2;Q MDT`Qbibx² KB`² xKB2MMQȐ+B U`QxT`Qbx2MBV D2bi rT`Qr/xQMv r+x2ȐMB2D

`QxbiĠT x#BQ`m /Mv+?X _QxbiĠT x#BQ`m  rvMQbB 53  `QxbiĠT x#BQ`m " `ƦrMv D2bi 29X q/² `QxbiĠTm D2bi D2;Q xH2ʊMQȐÉ ivHFQ Q/ /rƦ+? r`iQȐ+B r x#BQ`x2 /Mv+?- MDrBĠFbx2D B MDKMB2Dbx2D-  MB2 #B2`x2 QM TQ/ mr;Ġ rbxvbiFB+? TQxQbiƈv+?

r`iQȐ+B /Mv+?X qv/rÉ #v bBĠ KQ;ƈQ- ʊ2 H2Tbx² KB`² xKB2MMQȐ+B D2bi rxBĠ+B2 Ȑ`2/MB2D x Q/+?vH2Ɩ rbxvbiFB+? /Mv+? Q/ Ȑ`2/MB2D- iDX ( ^P

(x

− x))=nX C2/MF- MB2 D2bi i`m/MQ TQHB+xvÉ- ʊ2 bmK iFB+? Q/+?vH2Ɩ xrbx2 D2bi `ƦrM 0X .Hi2;Q- r TQ/MvK rxQ`x2 xKBbi bmKQrÉ (x

− x) bmKmD2 bBĠ r`iQȐ+B #2xrx;HĠ/M2 Q/+?vH2Ɩ |x

− x| B U/H T`Ʀ#vV x KB`Ġ xKB2MMQȐ+B #B2`x2 bBĠ rB2HFQȐÉ QF`2ȐHQM² rxQ`2K

d = P

i=1

|x − x|

n ; URXeV

FiƦ`² Mxvr bBĠ Q/+?vH2MB2K T`x2+BĠiMvKX Jv D2/MF #Ġ/xB2Kv bBĠ xDKQrÉ MD@

+xĠȐ+B2D mʊvrM² KB`² xKB2MMQȐ+B- iDX r`BM+D² Q`x TB2`rBbiFB2K Fr/`iQrvK

x r`BM+DB xrMvK Q/+?vH2MB2K biM/`/QrvKX

RXkX PTBb biivbiv+xMv jj

.2}MB+D RXkX9X q`BM+DĠ x T`Ʀ#v x

; x

; : : : ; x

Q Ȑ`2/MB2D x QxM+xKv bvK@

#QH2K

ˆ s

B QF`2ȐHKv rxQ`2K

ˆ

s

= (x

− x)

+ (x

− x)

+ · · · + (x

− x)

n − 1 =

P

i=1

(x

− x)

n − 1 : URXdV .2}MB+D RXkX8X P/+?vH2MB2 biM/`/Qr2 x T`Ʀ#v x

; x

; : : : ; x

Q Ȑ`2/MB2D x QxM+xKv bvK#QH2K ˆs B /2}MBmD2Kv DFQ TB2`rBbi2F Fr/`iQrv x r`BM+DBX wi2K ˆs = √

ˆ

s

Hm# `ƦrMQrʊMB2

ˆ s =

s (x

− x)

+ (x

− x)

+ · · · + (x

− x)

n − 1 =

s P

i=1

(x

− x)

n − 1 : URX3V .H rBĠFbx2D BHQȐ+B /Mv+? Q#HB+xMB2 r`BM+DB B Q/+?vH2MB biM/`/Qr2;Q D2bi m+B²ʊHBr2- D2ȐHB FQ`xvbiKv x FHFmHiQ`X qi2/v MDH2TB2D bFQ`xvbiÉ x FiƦ`2;QȐ x TFB2iƦr biivbiv+xMv+?X C2ȐHB HB+x# /Mv+? n MB2 D2bi x#vi /mʊ B +?+2Kv Q#HB+xvÉ i2 rB2HFQȐ+B dz`Ġ+xMB2Ǵ- iQ MDH2TB2D bFQ`xvbiÉ x MbiĠTmD²+v+? rxQ`Ʀr- FiƦ`2 b²

`ƦrMQrʊM2 Q/TQrB2/MBQ rxQ`QK URXdV B URX3V-  rvK;D² KMB2D Q#HB+x2ƖX

ˆ

s

= n ^`P

x

^´ − ( ^P

x

)

n(n − 1) ; ˆ s =

v u u

t n ^`P

x

^´ − ( ^P

x

)

n(n − 1) URXNV

S`xvFƈ/ RXkX8X .H /Mv+? x S`xvFƈ/m RXkX9 Q#HB+xvÉ r`BM+DĠ B Q/+?vH2MB2 biM/`/Qr2X .H rv;Q/v T`x2TBbxKv i2 /M2X

, j e N Rk Rd ky k8 jy jk j8 jN 9y 9R 98 8e

", Rj Rj R9 R8 ky kR ke jy jR j9 je jd j3 9y 9k

_QxrB²xMB2,

P#HB+x2MB rvFQMKv x2 rxQ`Ʀr URXdV- URX3V B URXNV  rvMBFB mKB2Ȑ+BKv r i#2H+2X

RdV.H x;Q/MQȐ+B x QxM+x2MB2K Q/TQrB2/MB2;Q 2bivKiQ` r`BM+DB- FiƦ`v rT`Qr/xBKv TƦʆ@

MB2D- birBKv M/ s /bx2FX