2315132
jqq
DVIDISIOW 513814 4O1TDA2T4A$1TDMIT2AD3$1O1
3VI223$1O$1OTUA
314T :2ETASIJHUOM
I4O1TASIUUJA14O1TI1I4OD
1nH
•q
ndo$1
!!ii51
.51,1lI3t
ÔQI
.oT413qa
nbhoW
HD51A32$1
DIMO4OD3
10
UA3SUJ8
JAT4OITAM
unvA
IJri3RaM
OOI
8EIO
AM
,bhdm8D
QQ1
1cJm3U
,igntO
3viID
,ickou2
nn,1O
,rbnH
bivBUxoD
bivEG
i12 AnErboi
Iil
bluow
ioiliu
dT
!u1U
iid1
tol
jiofl
toO
bna
bdqq3d2
1,WIx1A
n&n113J 331r18h2
emiT
33i*uwiiluM
no
n5I3mnoD
di
i
inaqiitisq
moII
b3vit
oats
tw
ainmmo3
4Q1
3di
bna
oiU
ns2
£imoIitsD
10'iiai3vinU
di
d
b5loanoqa
a3hicnonooH
tsi3n&IFI
bna
nsq
ni
b3noqqua
aw
ibts,ri
ff
.3iutu1i2o13iMthsM
no
,nt3mnoD
32YT4\AJDU\D2U
rkna3t
a'$138i4
lo
flq
ai
tqiq
auIT
.ôO1Q-232
maiD
nokj,thrwo13n!32
Lsnoiial4d
3di
lo
aoth
ion
bna
aiocftuafj
lo
aoc1i
ia
b,aa,tqx3
anoiniqo
'dnA.niaii1
taaA
ni
naiotq
.rbtaz51
31fn0n033lo
irn,ujfl
IEnoiisT4ixi
10anoi1a
riocl2
.brnai
aidh
hA
.llaau$1
.51ñ1t
bna
hn3
.1
fl3doSLd
IQQI©
un
iiii
bthivotq
rioiaairrnq
ii3ilqx
iiiodiiw
bJoup
3d
am
,adqziaiaq
owl
bx3
01 iOn .33100a 3111 01fl3Vi
5!33iiOn
©
nibubni
iib31
ÔÔQI
iqiq
nbhoW
$IHHMQ1
dfn3U
MOITDA2MASITOMITADH$IO
3VR23$103$IOTUA
HIlT
:2HTAH
JHUOM
MOITAHUU
JAT4OW1OD
TDAMTHA
ion
ob
iBdiiusb
lo
di
iol
!,bom
1B3iiaiii2
wn
aoqoiq
111wiqiq
iñT
no
aiab
LB
1041i
3nodq3I3t
,iBb
no!i32na1i
1i3nnu1
as
13u22Isrnini
rnJi
1up
iii
vins
I3born
di
,ai1na
thv131n1b3xfl
ol
3aainoo
nI
.lls3ino1ib
bI3sii
is
i&fiiiibomfno3
31obidi
bris
oiq
nhisv
3mii
3nasd3o1
Sas
€1J3v1n5noiisvido
nwid
rnii
cti
thi
(E8Q1)
nN
bits
nd3uST
sd
boqoiq
llsiiith
noii&rnoI,b
cnii
lo
13bom
iIi
lo
ihiq
,di
ni
i
,(QQI)
qff1iasJ
bits
xu5iuomsJ
(88QI)
boiE
d
buib
'1ini
iom
bns
(VQI)
hsID
io
sisb
visilixiis
5Iiup5I
ion
ob
lud
(IQQI)
!aiast
bits
1dO
bns
(OQQI).!s
i
l3IIuM
gnuii2uI3
noiiziub
iol
b3bivolq
i
nbiv
noii2
.wofl
ni
103iTh3
,rfi
no
noiiqrrrnas
wod
111wW
.b1sns
stab
noii3sns1i
1sinznfl
di
iol
tnnoqmo
aiiaini1rn3tb
£
bnosd
insflink
3111iol
tnuoos
11u13x)u2
ns
I3bom
3d1lo
noial3v
3Iqmia
iv
£
isril
b3iBbi1ono3
3111no
boi
Mifi
lo
bsit
n,,,v,txJ
anoiizwb
b3vdo
3111ni
anoiiSI3rIo3oiua
.I3bom
,dj
ni
3muIov
3bubni
01w
wo11
slab
noilsiub
3113lo
noii&rrio1nsit
31qmi
A
.13)hSrfl112u51
.51'i11t
31n3
.l
fl3doSl
8OO
,irnono33
lo
tn&niisqU
8OO
imono3
10
in3mtIsq3U
oiU
ns
sicno1i1sD
10'iiivinU
oiU
na
siino1ithD
10
'iiai3vinU
3vhU
namliD
OO?.(3vhU
narnliD
OO?.Q8O?O-E(OQ
AD
s11ot
5J
8OO-QOQ
AD
sI1o1
5J
5138
bits
OL ro ii flUOp2CLApJc CAGUt MPJCJJ W pG2t pG tJJOflJJ1 O 2 iocptic bLocGw JU tJJG2G C2G2 AGLk pJp L1C2 o cuATL? Jp12 wA G qnc to 2OWC flUO2GLAJC CAGUt 2IICJJ 92 UGM2 LGJG92G
!Lfl1.!f1!1J 12 tJJG C92G O 1LIJ2CUOU2 MpJCp 9tG CUCL9JJ?t 1ULGdrJGU1 pnt /#pJcp wA 2f1qqGIJJ?
q9A fGLG qcu1rG bcuoq Oj 2J0M 9CTh!A 9IJq MGCJ(GU2 91G bC9Jj? 2J011C EAGJ IJJOLG
iG cJo tpu iu rpc wiqq
o
tG q9A ho!. cm.Lcuc!c2 iipicp sic twqcq titcutA orn porn bcL
rLsiJ2c11ou2 uJ9A A9Q OAGL IJLJJG hO!. 2t0CJC2' I11J29CtJOU2 siC WOLG pcdnciu ucsi rpc obcu uq
jpc bLOpJGUJ 12 GACIJ WOLG IWBOL(9IU iipcu t 12 LCCOJC rpt rpc ji.cdrrcucc2 o
iiSU29C1101J2 q9w JU IJJC JL2t bJ9cc
tpCLG HJJJ pe
q!.9uJ9tJc J022 O iUOUiJ9qOU mpJCp Uf9tC2 rpc 9 Ut9C2 O WOAU O
tOO 2JJOLt 9U WCLA9J J2 2CJGCtG UJO2I CGJJ2 114JJ pc CLO pm tOO JOUR 91J UtGLA9J 2 CPO2GU JJCU
2tOCJ2 M!JJ p9AG tWIJ29Ct!0U2 GACL? GM 2CCOUq2e JJCUCC 9 UJfICJJ 2JJOUGL IIUCLA9J 2 9bbLOb49tC II. LUJJt pG WOUflJ2 0!. GAGU ?G912 ()U tJJG O(}JCL GXI1CWC 2tOCJC tLSIJ29CtTOIJ2
oi.
i.cdncuq? iqcq
tL9JJ29C(JOU tLCdnGUC? ho!. brlLcp92c2 0J COIJ2fIWQL flL9JC2 pX 911 T1JqJAJq119J utrasj urcus-j
botcurwjjX Jwbou9ut b9U o tpc 9u9J?2Je 2JUCC tpc 9bbLobi.!91c utcuj iijj qebeug nbou
tO CJJOO2C 2OWG LIUJQ JUIGLA9J 9Uq 9LG?91C ipe rL91129Cr!0U2 OCCflLL!1J M4fJJU (JJ9tUtCJ.A9J
JJJ2
91J9J?eJ2 sic pcq nbou cdns-jj? 2b9cGq qr tJJCLQ !2 9 utImj !ucJusuou pA tpc GCOUOWCUJCJS1J bsurcnjsi W02t tL91J29C1JOIJ2 q9w 9LL/C 9t !11tGL/9J2 BGCI2G 011!. 2NU9L wctpoq O
JJJG 9U9JA2J2 O 2riCJ.J q9W 2Ct2 bLG2CUt2 UC/A 9IJq JUtGLC2t11J CCOUOWGtLJC Cp9JJCuc2 P1 O1CL qc1cLwu91J12
to woqcj s-uq OLGC92t pc pcdncucA uq qaipnuou o r1.u29CuOu2 bo27!pJA 92 9 fluCL!Ou o,
tThc2 OJ tL91J29CI 0112 /ApJCp sic 9fltOUJ9rJC9flA LCCOLG pA COUJbflICL2 QCiJCL9JJA (JIG Op1GCCAG !2
UJICLOCCOUOI.UTC (L91329C1101J2 2flCP 92 ICJGbJJOUC C9JJ2 bracps-2c2 O ItGW2 011 CLGT( csiqe 9uq OtJJGL 9U29CqOU 11112 1111111 92 UOM CGIJ LG9CJJG I. UJ9IJA IJU9UCJSJ q9W 2G(2 92 HGJJ 92 JOL A91.Ofl2 9(9 91 C/GL p1JJCL JLGdflGUCJG2 JJiC flJITUJ9IG JU pJp LCd(JC1JCA 99 COJJCC(OU LCCOL2 GAGLA ffitJJ (JIG 1UCLG92TU bOMci. 9IJq WGUJOLA o couibcl(cL2 it ! U9IITL9T 10 COJJGC( 911q 91J9JAc
LG2GLCp qccqou2
C112 OLGC2t!U f12J1J VCD woqJ 2GC110U JØ M LM COIJCJfl2OIJ2 911q 2CuI22 flLfJLC
ij bi.ut u
woqj to picjnqc driunr?% cjc u VCD woqcj ccuou
q12cnGq poA crJou itqj bLGcut 2OWC
C212 OL IJJG ffi U2CtOU2 qSI 2Ct!OU g
uioqcy ?CCI!OU Q MIfl 12Cfl22 C2UW(JOU uq bL2cut cxuJbJc2 nii
rrn' J!uiG
LG22Ocq P IIJG VCD WoqV 2GCt!OU ? iJJ PL!JA I!2Cfl22
C!UCt!OU tpC VCD 2CCrJOU MJJ 12Cfl22 bLObCUJG2 O1P
VCD WOJ 2C!OU f M!JJ bLC21Jt tp jccpJJOOq rnJcqou
1 IJJC OJJOMJ1J 2GCVTOU 1G 1UOLCL22!AC qn1.ou (vcD) woqj irjj pc qcicjobq
rnocoucjnou iu 1Jo-LqG qnurou Cx!2r
MG GXSUJIIJG JB LU2C11OU2 qw EU 9tGL ipc 1UJG o qA cct buijcq onte ji
jpcc
woqcj 2flG2V CJn2iGuu o qp CIfl2tG14U O
12 bLccr2cJA iipt c uq !ipGU
(j,)
tjJ qf1Lt1ou2pcrMcGu rLIJ2ct1ou2 wA cai.) juomrnrJou pont rpc 2WtG o tp wijr
bLobo2cq pA K?1C (J) vqwr1 iiq crqGLcL (jgg) 9uq WOLG 1.GCGUflA pA E21A uq
OH'-LGCCIJt LCJcruqJ1U O, HUGLG2I flJ tpG LIJTCLO £pGOLA rniorrnqiu uucj riuscrjou qw
v-MIII G ET1J1JC1I tLU2C1101J2 qt 12 b icnjqA 1U1CLG2TU tO CXUJTUG Gcfl2C O tpG
jo JJJn2PtG rpc i.uoqj -uq bLoAiqG u cwbJca
uectioue qw pow Iju-ucJ W91J(Gt2
UJOGJ2 12 1UJUJGq11GJA botiuisjjA LC1G)1Jr
!WGLAI 12
rniiiA rponpt o
qrn.riou it 12 CJG21 qsi tpc A2f poqA o LG2GLCp ou qntqo
tJJG JC1JtJJ O tIWG 2TIJCG tPG bLGAJon2 USJJ2Ct10U IJq IJA 01GL Of1t2G UUflGIJCG2 V2 cPU.U2Ct0U JU cp pJ21ut oj trwG
tpr2 bLopp!J!A conjq ,i.A ittp rp tThc o au2crou
J!21 0J qrmtJou2 uq Cp9lCtCLT2tJC2 O GCJJ a1J2CtJOu JJJt
tJJGLC !2 2OWG bLOppfl!A o1UtG1J fG1MGGU tL1J2C1JOU2 G Luqow AupJc tO G ujAq JJJJI2 IJJQ qt 2Gt
CCOUJG2J2fG O 2GJGC13IJ
jXGq JU1LAJ 0L 1J9JX1U tJJC qt C 12 bLobo2Gq to IGI IJJG
O tHuG U0M
OPA2GJ2 1Jq 1'2T (j) prir qo uor LGcJTJJLG nxJJi9LA qt oz. 22r1wbpou2 ou rpG C1J2G2
uq Jtt2 (Jo CJtJ( (j) uq UJOLG LGCGIJqA qT2CIJ22Gq pA 2tOCJC (J I1JJGL GI (JØ)
1Jq tJJGLGOLG 12 ru rp 2b1ut o rpc woqcj o ITWG qcournrou TIJIPJJA bLObo2cq pA jncpu
CflG VfltO1.LC22!AG ouquouJ Drr1qou jjui bLocGqn1 uJOqGJ2 tpG uwc J1GLA2 qjLGcqA
JJJJ2 bbCL M!JJ bLobo2c u J1GLJJUAG to xcq IUtGLA9J uA2iv JpC bLobo2cq wtpoq !2 MUll urnuX nU!UOuJrnt1/G qt bO!U12 01. q2f1i2G qJG bG4oqa O W02t IJIGLG2t
floiiEIUImoJ
I3boM
.
{
,j
,...
, }crth
bfl3U
a
Lqrrüa 21rbirfw
zo1q
asbo
rfi
1bi2rioD
Iav?ria"b[th3
ia
mii
3th
baa
"oiq
inioq'
a
bIth
ai 21r11cnu1
ci
biudhiaib
alnioq
1a
(i)M,2ao1q
rihrwoo
£
21 2m13 LsvFnath
oi
nibcioqnoD
.o1q
lnioq
di
bomi
-non
a
i
()M
IaijoivdO
.jcmii
fi
'cf
b11t33o
vari
rbirfw
1oidmun
th
i
rbicfwlo
noiarnqx3
Ianoitibnonu
rb
n11Q
.aq
tinu
th
2R513fl
tacit &cthlo
noii3nul
niaib
:aR (t)M((t)M)a
=
(t)A
(1)
lo
qot
th
ci
.15wiI
ci
bta1i2uIli
2izoiq
inioq
di
o
noi1a1noiqi
noiixiiñ
nitflUO3
rfF
!ainv
ci zaH .1mi
d
b5rIuxo
3varf iarLi2Jn3v
lo
idmun
rft
bsznwIIi
var1
w
5wi1
rli
.inv
cia 21n231q5InoitrwI
qia
21thno
qrnu[
Iqmsx
iol
ru 2S2rrrIi
cr1O2nuIb
01IU2U
21 1122)Oi
DL12&13012 2irbaidiib
5io1H
.(QQ1)
3WOIObOT0<3
aa
iol
baa
1
iruoq
aa
ta
Ii
"2UOuntnO) I1a3i12ad3o1a"d
ot
bia2i
2a3o1q
2111T0
=
0
<
(0t)M
—(i)M}q
rd
()
arrib
lo
idmun
tinfl
cit
ic
Ii
"trIcni3ni
tnbcqbni"
3vatl
ot
bniIb
21223O1
rfT
Idshav
mobnai
u1t,t>t>t
i)M-(i)'I
(0t)M
A
".22301q
no22lOq"£
blls3
2123nar1t3a1arb
32ci1lo
thod
2arl tacit223O1
A.1nbnqbni
ia
=(t)A
fI3irlw if!223301
"2U0fiOfn0fI
mh"
dI
21aao01i
no22loq boqi
iriinvno
IIaIu3inaq
tariw
d
aaoiq
euoriornorI
3m1ta
olili
b&moIansit
d
na
230q
no2aioq
'dnaia1
ci
•
.noitsrrriohbmit
iiainirrrib
£
bILs3
d
idirrt
d
01atab
noLJoa2nalJ0
aqst
th
iol
3BnqoiqqE
222301q
f10221oqlo
22.E13cIt
21 IUHlo
rioxtqmua
ff1
tud
2u0u3Onrnama
iiunuino
a2arbo1a
lo
noiiqmu22ar1f
cbcuraax
ii1sIu3irIaq
ci
.22233o1q
2noIt3a2rLc1Jiom
ioI
3Ldar1oit2up'hBl3
2i a?rIcr15t3ni3flbn3qbrn
lo
iiibncpbth
i
bohq
3mil
wiu1
£
ni
noi13s2r1s11lo
dmijn
rli
lo
noiiudhlath
rL1 i&LiiLqm1
a1
fbirfw
aoq
£
io1
floIiqmU2aE V113Sh1iBfIU'1v
S2
2irff
.325qr1i
ni
isi
noi
sanS-rirfi
iqox
fbom
ol
nithon
ai5ith
31111$i3na3
.noiosn1i
lo
rIup5t1
th
I3bocn 01thu
lo
2noirsifqmi
di
aisiiauffi
.131ul1
lo
monod
r1T
.mb
lo
nOii3nuIoiiainirrrib
£
eq.srhq
di
c223o1qn1Jnuo3
lo
2noiIEiIB5Iowl
ia
(i)4
bris
(i)M
Ii
lS1u3irthq
ui
.noiiqcntJ2asf1
i
qo1a
r1T
.(i)A
bLds1
3ni1th
d
irfim
I
cmii
IS nOiI3nLJIn3nuo
r13 10uIsv
biqx
inbnqbrii
lo
noiiqmuas
3d1bnu
inssano3
airhiriw
a1av
lo
[vi-ris
Ia
iLt
.a1nrn5I3ni
d
ion
btuorfa2noiisiub
io
1vith
tcth
z1Jqrrii rioiiqmuaaBrfi
isJuinsq
ui
1oi
MifI
ii
ioJ
.bvocrii
515 21nnoqfr1o3 312nrrrib
'ns
iiIs
iasI
Is
b1SI5rio3oiuS
2r1oi1S1ub 3rhni
IoiisLsno3oIus
lo
sn1biv3
isb
aisicü
woEd
bw32ib
d
oi
anoiizsrtzil
.mii
lo
2rIoil3nuI 3i32ifl1rn1i3blo
noiisnimiI
luodiiw
io
rL1thW
01IJJI2u
211122301q
n022j0qrf1
lo
2fl0i1Si1rig
uboiini
01ibo
uI
s
(1x)13nflb
bnis = 1xd
noizuib
th
r111J
.2rIoilSwb 3n11lo
L10113nU1'Ii2nb
'iilidsdoiq
22501q
0221oq
2IJonomof1
rni1
£
o1
x
lo
flOii3fIUI'Ii2nIb
viJSIumuD
n1T
.1xlo
i1rib
di
:rmol
r1i
asri(—)qx
—I
=
=
(>
.
(E):jsrb
ioM
.b1udhiaib
IJ.s3iirIbi
bus
1nibnqbni
sis
1xils
rrfw
Idshsv
mobnsi
1sbnnoqx
us
(xA—)qx
x
()
—()oWI
=
(
x)J
notiqmu2s
rh
ibnu
anoiisiub
Mlo
[qmsa
3±
lo
baon[i[1ii
o[
3d1 aiJ
noiazslqx3
3zzI3±
\
T4 ailo
JM
3nfT•2201q
022j0q
2uonornonf
s
sis
rfj
isth
iIuqoq
l2om
3rfT.2Hqa
ivo
iv
01 woll.so
1born
2iffibriix
03 IBWIBII eiII
io)
wonox
as
bisi1
is
rbhfw
ithsvo3
ouboinii
ol
i
(VQI)
xoD
d
b1u2
rL3Eo1qqibrfl2
3rnonoa
lodEfnI
.((8Q1)
b1d3i$I
bnB'ibnH
1n3
m
as
2uonox
"bth.wt'
io
(88Q1)131i)I
3Lqrrlsx3ioI
.ii,noiiri
3IdB'rIdo
ioI
b3ubornii
ts
1d.hsv
as
nnhw
i
has
Ibom
bisxsr!
Lsnoinoqoi
rfJ
bII
ai!bocn
rfT
.2vw2
iol
(OQQI)iasrnsJ
sqx=1
()
rLi
izid
ion
2ob
noiizno
2irfT.Hq2
difj
oi
ishqoiqqs
1udiiim
lo
ioiov
s
s
5Idw
d
ion
io1irh
fEw bIts,2'
th
no
IsrIoLlthno3iasL
is
3nbfIqbrü
is
2noiislub
isth
noJqmu22s
.sisb
2noios2rIsli
3rIi
iol
IdI2233ua
oirn
3nbn3qb
&rthni3ubo1ini
tol
51uist3i1
f1
ni
2flOi2u2
owl
IaSI
is
ts
tr1T
35113032
'1duob
rb
21 32111r1T
.mij
lo
noilDnuI3iiinirrr1ib
£
31rib1srn
'Iqrni2
iriodiiw
its
d
bsIqi
212s
ith
ciT.@V1)llbnziO
'd
bibu
as
(sVQf)
xoD
1001q
noasjoq
rfiiwisb
oi
if
u31IIib 2111Ibom
3Ldsnoast
s
ma
airfi1isfW
.2ot1
no2aioq
1'I
aiaoizqmuaes
3f13bnqbfli
rU
torrrtc1rwI
izsio1
bits
1srnb
03xLqmo3
21bits
ff3
old
2noilstIJb
bsI
1B1oqIo3ni 01 21(sVQI)
xoD
th
nOi12u2
bno32
A
.bisvkiomnu
3r15rw3rb
3nuI1th
01onh3qx
in33I
2woHsthiT
.l3bom
btsxs11Lsrioirioqoiq
rfi
lo
to33v
(08Q1)aszoa
bits
rIsrnI33H
d
23J3rnono3
oirü
buboiirii
iw
qi
airit b2fboM
.btsxs11 3n5r1u3no
3nno1qmmJ
iasq
lo
iosqrriirh
nirrisx
01tdio
noms
(18Q1)ctsrroI3H
bits
rii
isrli
o
2f5ubivibninsm
no
ah
3rrth ilofI2lls3iqi
51Bsisb
rfi
21bom
th
nI
.anoiisiub
bwasmnu
I51rn
to
nbnqb
31B322iDfl5I
'J.mni 21113irfir1w
lo
noii2up
insfloqmi
tv
2mo3d
boorfibAifiniot
rli
lo
anrii
ciibatqx
d
21IJO3 b (153 21f13O '(I5fflbrts
21bOm
2dT
noii3nr1
(e;1x...,1_xi1x)11goi
=
=
(8;x,...x,1x)
di
ni
hs1D
.'Liotib
2booth1)I[!Isnoiiibno3
ar1i
rrimstsq
01b2oqotq
5ir1
21ii
at nOIJqmua2stsw
1311351A
.()
nias
Isiln3rIoqx3as
21 boorIi1li.1Isnobibno3
rbs3
3253
022j0q
132noiisrrriolni
iasq
3111 aqsrri 113111wi
noil3nuI
£sd
bhsmrnuz
3d
ns
33n3bn3q3b 3rrthr1i
isrli
uq MTJJ p/ w9ii?' o rpc wc bLobuJc2 i'r H tPG ovJcH(JT) oru ooq 2rUiIJ
1.Jsr1ou2Jnb ro woqj o couqrnouj AuuCG J VcD(JI)
JOOfl2 O OV1CH(JeJ)
JGGL2 MJJO LQ WFt N!1P
V1CH CJ922 O woqcj Miff niiij)
ccou
rpcj o ih uq 12 fCLC0LC con IJIJrJ? jpcjcq VCD(JeJ).
au2ciJou cu p cowbnq qn.cqA L0W (o) uq (Jo) jjn woqj 72 oujA ou j o x uq ou
0LQC22 o qrnou cu G cowbruq qucrjA
jpr i
tpc cxbcq qm.ou o, we
q2beL2iou41
20 ocu uoJccq In qnrrou qr aerv ELOW an Lcbecq cxbccwou2 UJfJJ12eb
JjJ12 Mpcuc/ei. a>o we nucouqrnouj 2rmiq9Lq qcA11ou Mrjj cxcecq w weu GxJrprp1J CXG22
(ii) Q5
MJJGLG
<j nhJTJLJA qJe couquiou AL1UCC x 12 iK pin rye nucouqponj iuuce 2 JAu p? a
SJrJJOnJJ IJJG qXiimiic 9'UJ?2!2 rn rye bLoo o jcnjw ji neeqcq
O yJme rpr r cqr iipcu a+
oi(j-c-)Pr jjn 2 W021 eij? ccu pt
rpu
CXBQCrPOU2 o pory 21qe2 o edriou (jØ)
cxwbJee rye couqJrouj uieu
o
x' 12 IWryeconqrious qrrLpou pin rye rrucouqrnou megii 12
JJJ12 woqej 12 C0IJAIJTGIfl pecric ir JJ0M2 AL0fl2 WOIJJCUI2 ro pe cjcnjreq pX cxbecwroir EOL(To)
'>O Ar !=T4
1=1
()
i) ZJ!
=
joiK'
+—-v
2rwble ACL10IJ o fpJ2 MJrp cxboueurij qciq0n2 uq bi.wereieq IJ reUJJ 0 it=y
ro cjj rye woqej fnrOLeLe22ric COuc1moUT OLVCD
uq iK ci pe ceq rye couqwouj qrn.iou uq uce qcbeuq2 ribon b2r qIfl.S!OU2 1 2 irnrmsj
()
E[XX'X'e]
=
1K!=
()
(x!\Jt,x!_Ix8)(xr\JK8)
nu!r)
jjrnr 12 rpe qeu2irA o rpee 112rqqeq qr1LIou211 2u2A:
(j) iK' =co+coc +biK''
\
(
(J) '
— iK!\
JA2
uq 2fl2Ut1tiU
(T't) I =o+cx'+4'
/pGW
L()
a rpc
ww riucuow
rp
nucou
4 2 biiwrcicq
oon?t o (jç) tpu
(J3)
E(X! 1)L(T+ }
EOL
iJJJ2 woqj
cxboucupj
qcbGuqiu OIJMJJC[JJGL )'. 2LGtL
OLJC22 Pt (IUIA LC2bCqACJ?GCLGVIJ JJ9Lq
J1IJC1JO1J2 jJJ12 WCC2GthCJ9flA JO1JqflJ.To1J2 1110W OL JG fflCGJA 191J0L
(JJGjp
couquiouj
quitA i uoi vto b1.wcrL i1uJi picp Cu cxpip GJtJJGL flJCL 1J OL
x1
4
(is) )
= T(J
Gxb{_(J }
0L
X >
bc IPTJ2 tG couqitiourj qcinuA
ts?. to qccupc tpi 22nwbtJou i vpi (xtj 12 cxboucuuj
w2rn.pjc rncnou oj
JJJ WO2 bobnj 12 fo 22nuic rpt rpc couqipouj qitupniiou 2 fiGflff ju (JJ2 C2G I12I1J
qCIJ2A U () 22flUJG tO p GXbOUCUIWJ Put JCL
C0(EJC22 !AA2 £0 '-1ff £J12 LC2tIJCtJOUJJJ 2bCqjCr1OU2
() uq (To) cu pc ujq iii uJ1A ,iAa jp couqItouJ
ounijjA pul.oqrrcGq pA uJG(Jg
BOHGL2JQA CPOII
uq
KL0IJGL(j5) g BGL 9uq WIJ2 (rY
.u VJCH
uioqcj it
2rILACA2 OLY VICH woqcj uq J!t2 O I!UGW1J1 CJ22C2 2 B0llCL2JA EUJG uq J2oIJ(J4)
GIAQ IJJ0QJ2 0L A0JPW2 £LQ
J0t2 0 rn1GL2IU bo22pJpc2 pCLG hOL WC1Jt
b0rut
tPG VCD(JJ) 2Uj r'j
tuiu
boiur
H0//L 2 £pW 9W ALA uimA
51311W
(k+f}J(1)
k'C)
k.v)
.(OI)
2E 3111 'L13sx3 aifbidw
at
i
3viiEm3iIB3vi3rnE
ciA .3ldi22oq SIBanoiiEDi1iq2
3h1&nslBqr1io
nsM
SI3rLIibrn2
'nEm
ni
bu
brIBb32oqolq
nd
acrf 21111 3LiffV/.biBsr1
3J3rrIBlBq-non
£
3i13mi23.IIa&bor
3mii
ivo
hsv
b1s.Er1 3rIi rbirfw ru 21othus323±
ol
rlworDi 23IqrnBx3 ocxsui
b3brI
3dT
21111at
I3bom
(iDA
3±
bnix3
03iIufl1th
3dion
bhiow
ii
1fl3v4
tn3bn3q3bni
3diliw
Ax
ri3±
,bnuol
21F
ioI
foils
i1i3q2
3)3TIo3 3113 rl3rlwicLi
21nobqmu22s
rns1o12r1
1orrnol
3rno2d
b3iscrü3a
3dns
a3JdshEv mobrust ciua
lo
noiwdhth
orfibits
boorfflffl
d11s
bu
3d n3rfins
rnsioithf
bismim
2rfl'
.I3mI
io
3niIq2£
s
rbua
ioismii
-irri
3111ol
b3isIsi
XlofD
i
sruboiq
311T.ii
iii213fit5lS
3r13 335m1123-31ol
noiizrxrñ .(IQQ1)Bivi51-s51s.cioObits
frt3
d
b3isrnhi23 I3bocrx HDSIArimisq
A
.bihirx
'Iias
3doats
ns
noiistub
LsnoiiibrIo33±
lo
rioilsfibqa
3irnsct'b
3dT
:3dbluow
nob
i1kqa
isni1
pct)
+
1ii1E
+
q_jXqD+••+£_1xn
+
+
w
=
y
(Vt)
ruas
a1cIsi-rsvl5dio
3bu!3ni bluoDii
brus cuolionul Is3ruiI-non Bd
bIuo3
aidIIst3n
sioM
=
1jJ(81)
HD51AOM ,HD5IAOAHD$1AO3
3113 03 2UOOLB1IB al3bOfrt a3buI3rIinocsiui3qa
£
rbu2
01a3ldsrrsv
ofrnono
awolls
ii
Irth23131ni
3loM
.abiIidiaaoq
as
213(110nsrrt
bits
HD$IAOT
3(11lo
flOi213V 21111m011
.aflOiiDfi2fIBlllo
'3fl3tJp5ft
3113 a3rtirrrI3i3brbiriw
noiIsup3
3(11 131(13 ai airfl' .2n011352n5-Ijlo
a1si
3di
lo
alnsnrrn3l3b
3iffl0n0z3no
2ia3rboq'r1iai
ru
ruo
I3bom
(i3v
I1siJr133oq ziii
,au±
bits
n3lsn3brIu
fIi3d
ai 2I2'IBrIB 3111'dw
fl02531rism
31111dsdrnq
.b335m1123bits
b3fliD3qa 3d bhiorlaa3Idsnsv
(I D112wed
l3biaIIoD 03lnsnoqmi
b=d=j uq (a÷t)
+ai<
jèIpGIJJ-UJUJ 3: uqcL IJJC cOnqJnOu o JGWW I 9iJ MJJCIJ A(X'I') cxJi uq CdnJ2 KJK uq MGU
IJJGTJL2IOLGL C2 !U fG OJJOMrn 1GWW
2!UJ!W LC211J12 C9IJ pc opcwq OL 1JJL WOWCU2 gJlponp ,tc 2wpJi2p lG2 OijA OL
ybbcuqrx
(3J)
um7( d)y uGcc2&LA couqwou rp sjj IjiG L0012 jic onI2JqC tpc flIJt CLCJQ !2
i
(30)
=
rc'
or1lJqQIJJG (lUll CaCJG ipcu X COU2I1U nucoiqwouj W91J J/GU pA()
u{b3}
uq r jj IJJQ LOOf O I}J cdntiou
iK' =M+&X'
i-'uJw- p llE(X') GX!E12 lJq GdnJ2 iW
M!JjpC cou/GujGul OL qw uJA2r
1p12 cnou c qcAcjob bLobcw o qi nucouqiriou-j uiowur o '- VCD bLocc- jC2G
DCLGUrqU MJrJJ LC2bGCC to o
(t) lie) =
HCUCCrJJC )O!1fl J0 j jpooq jnicqou 0L tpc cxbouGur!J ACL2JoU cu pc MUtCU
2 rp bLoqnct o rpc couqrnouj JryCJipooq
C11CLJ X' MJfl Ijot p niqcbCuqCurj) qiruprncq jpc opu pjjrpO0q nucriou cu JMA2 PC
fl112 2GCtJOIJ Mrfl qCACJOb IJJC JTJCJTpO0q (3UCfl0IJ2 OL tJJC VCD w0qcJ2 qcctpcq poc ju
f JJJC rycjpooq hmJcf!0u 0 U VCD OJ
JJJJCL OLcJCL woqcjv
2!1Jfl1
Jflt IJCLC2JUJ?C0WbJJCrCq GXbLG22JOU2 CTJ PC oPtIJq OL t}JC 1CL WOWCUt2 iiq OL qrmrou2 JoL tJJQ JCrprijJ Mitp BL1JJCLCL It CU PC 2OM1J tpt110 CXCC22 qT2bCL2JOU IU LpC 2W1JqLq qCAtJOU2 CACU tpOfIJ tJJCLC !2 1J (JiG (flJC0IJCJ(!01JJ cJI2bGL2JOU fJJ1 12 tThicjj? O2CL/C in qriqou qw hOL IJJG CXbOUCIJtJ9J W0qC 20 LJJCLC J2
rpu qoC2 (JIG C0UfltJOUJ 2WuqLq qGAJuou JJ112 woqcj tJJGL0LG 12 C0U212(GIJI M1p(JIG GXCC22
flJT2 LC2flJt 2JJ0M2 VJrnt (G nucouqrnonj wuqiq qCAJiiou GXCCC2 (JIG WGU fD? LIJOLG
bL0O: 2 bbcuqrx
Ij—(c÷t) —cx.i
()
A(x)='1K1
(3d)
(33)
(('"
(31)
T1)'J
D!LGU14U MJIJJ L2bCct to )% uq o
(30)E°'
HiVCD jO JICCJJ]JOOJ TJIUCIJOIJ 12see. se
()
J9J9J!
uq
rp rnoLwiou wrjx cu pc cwUJrq pA
qerupnriou uq cxbGcriou o ou p i A to
pr fG coi. itjj
pi
xbQcrou O LO
fluqcL coacci
ciIjcuou rp iuqmq1!cq
cuc —r. r nq
itrp 91J
GXbOIJIJrJSj JJJJ LGCIfl2LAG COW TJIUCI!OU 11T0Ofl2 t0 tP 0 BOHGL2JGA4 (JgQ) QVJçcH woqJ()
s
=
x
x'
uq
()
/I4JGLG(
)
9O281
It11Ih 99
Be Iit]it
se
soQ
9J!
9O(it' )IK' 98
(32)
jp bciou O (pC HG221J 12
4'('4''\ (\28
(' 28 28 1
TjA)V
(!
T)WW I
I: JJ
28 ITTi
\
Jj
S Jqi 2COLC 12 GLO jp H22IJ CIJ pc
p?
12 OUCe 1 C p 2OU c xbcruou o
wouu tp rp couqiuouj xbccrriou o
q 8
12qmcq 2
()
2828
(! (! 28
((! 28r' 281
T) rJ
w+R_T)
'JT[TWj
21
uq
(2-e [(fl
[ (4J
'l2e
1.)
=
TT)
+
JTjV
L (33)2A
—(. (4,'
+ ( ()J 3
jcnjucq unwcL!c1J1A n2iu pcwuc
g-2dni.q OptfluGq GLOW LGLC2iIJ ACCtOL O cuCL9J1cq CLLOL2 qqmCq 2
JOL £C ExbouCurJJ uJoqGJ1 IJJC fl' C2I
PC LGflCC to C IJ..1J JAJ MCLC } !2 (Q
pCtCLOC1JCJO OL CXCC2 q2bGLJou ru rpc qnriou J!rc1.tm.CuibflCq
p? tpC woqcj ebCcuc!ou
JJJC Jt1CL £C2t2 LC JCUOMU 2 £C2t 0L nuCxbJ9TuQq £C2t OL UJOLC CIJGI3J 0UJJ O WT22bCCJIjCrJ0IJ MTJJ J0OJC t qGAJtJou2 tLOW WOUJCIJt COIJOIJ2CXOCUOII ALTPIC flcp 2 AOJfTUJC buc OL bLCq 1J IpC COUIGXt o ijucij qt r
couq
LpJC2 p3 (JC COUtCXt 0 uuCJ qr 2Ct2 MC UJpt flJCC £0 £C2t OL IJJC OLUJ22JOU 0 MCJA COUJC £0 wTuq f £C2t 0 bLJUJSL? !IJtCLC2r
£C2t 0L UJI22bQCTIJCJOU u ip oun O owttq
BWtiCP uq u(jg oqc(i To8Y uq EuJc(J yiA boaJpJC £C2(2
JJJC F 1IJC fl1PbpGL £C2t JJ2 bLOAGU to PC (JCfJ IJO2t1C 00J 2CC OL GXSIIJbJG
2bcciUctioIJ JC2:nJ fl2TIJ FLU YTBJ!BJ!CL LG2f2•
G2fUJ1G EXbOUC1Jt!V £IJC bwL 8 '4JJ PC p!q
C2UJtiOU O £JJC biucicL 0 s-uq
hTJLrJJCUIJOLCe r £C woqj MCLC £LIJJA MC!prr]-J uq ouc CCI2G fpC O qTOIJJ CJWGLJt Mill hOt PC CLO CUC1CIJt C2UWt1OU LCdflJIC2 tCC Efl1CL COU1J
E[& (&)]=
(A)cxb(—)qX
=
J—CE{
(&)]
=1 A()
Gxb(_A)qA(iK 28 98
(ag)
A )24 24
flUQL IPG I11J Q =0
tG
pjocjc qiou-j MU Lc2bc1 to rpc qqwouj b9lwcrcL
(i) b(X' e.XQ5) =
Jo((x'
))
+
io(i÷._( '))
JJic
ucwpq ryjrpooq nuctjou cu pc bbLoxurntq pA
CXCC22 ptcLOcuc1tA iu rp pq 2bGcrcow
tG2f p2Qq OIJ tjJ riti tG2t nJItJX bLobo2q r'uc2 L(1o82Y .LPC t 1°°Y OL WfrJt1bJTC1AG
JCIJOMIJ 9 1G2i2 OL GXC22 qT2bcL2iOu oi nuxbjnicj p LouGJO JJJGLG 12 g 2JUJbJQ OLW O rpiaiijguc itqncp ponjq p dnj to ouc pJ rpc qrirou JitcLfnLc t2t o Lp2 couqou
fluqcL couct 2bccrIjctiou fpc wC9u o tp cuipq U.OI.2 porijq p GthWI to qic
IJCLJ r' (2t 0L IpQ J1Ut!/ 0. VCD(bd) bLocc22
12 c2JJA 2OMUJ tpt1fl21 2 OL QCH woqcj uq qçj woqc c cu uoi qcLAc
ipc nnj cpi-2dnsTLcq qitupnuow
jourpuJ tjccu pow rpc wxruinw Jrj.cppooq rrurntc
fliJqGLtpc unjç jjJc c2t wtT2tic MJfl pic
t ipe UIJfl
JJJc -2dn1cq CU pc opriiJcq LOW tIJG 12t J1CLOU O tpc BHHH
c9JcnJ9tcq pA 14*I5 MJJLG J 12 rjic J-2dnLcq LOW LCLC221U AGCtOL O OIJC2 OIJ ipc 2COLC2J0L pOIJJ tpc M!P1T siiq Ipe EXbOucUr!T1 I 12 /!Gfl aJohw qrnr rpc rvi 2rtxpc cu pc
M4JGL pOfJJ 91G cAJnrcq i rpc unjj
(
,to)
{iK 9 jt34 2e
21K'T2!K
OLJ tJJQ AGCtOL O buj
Cfl2G 12 AoJtJJUA cJn2tGuu Ju rpt C2G uq JurcLAJ 0LqT1LtJ0U CJfl2tcUIJg HI tJJ2 C2G
bo2ifi/G fltOCOGJJOU2 LG bLGCI2GJX Mpst OUG uqa OL J110COLLGJ(JOU2 0 2d11LGq 1.GUTLLJ2 JJJG
LGIGCtGq OL pO(JJ qw 2G(2 pacq 013 ipe CL1t1CJ AJf1G O 54 t (PG JGAGJ JJJG2G JOhJ 2G(2 O
r'flU-BOx 2(S(J2tIC o T08 uq tJJG 2GCOIJq 0 5J JJJG U(1JJ pAbOtpG2J2 O MpUG UO!2G 12 G92rJA
bw2Gucq III 1J(1LG 3 B°tP O IpG flf1U-BOX 2Wt12t!G2 LG iA
JJJG JL21 qt 2G( JJ2
JpC (1(OCOLLGJu(1OU2 iq buij fl(0C0LLGJ(J0U2 0 tpc qm.rou CtMGGhJ LuqG2 ic
(JJC2C qw 2C(2 CJGLJA GXJJJp1( CXCG22 A'LTUCG 113 qtOU2
Ijf1LG 5 LOL g
J)0122013 bLOcc22 rpc UJG91J 2pOrIJq pc cdcwj to tpc 2tuqLq qcAT(io1r BOIP OJJJG 2(1JL qGAJ(Jou 72 3Q 2Gc0uq2 r
T21OLW
OL G2G tJL1TOU2 !2 Oil (G PO((O O
2GCOU2 MJqJ UJIIJTW(JUJ 0 0 2GCOIJ2 uq UJXfl1J(J1JJ O f3Q 2CCOU2 OL lfl2t OAGL UJIIJ(UG2
E1nLG 5 bLG2GIJI2 JJJ2tO1W O (PG qflLtJOU2 JJJG 2CCOUq 2UJbJG
IJ AG12G O 30
J WiUn1G2 JjJG211JqLqqcnou 12
2GCOU2 uq IG 2)(GMUC22 12 53 jpc tob bou Oh O
IJJTUTIJJfIUJ flJtGLAJ 12 0 2GCOUq22 SiJq (PGUJ)O1JJ(1W W1G1JJ 12 2GCOIJ2 OL 1(121 OAGL J OflL suq
JJJG 1JL21 2UJbJG p12 1J AGLC 11JJG JU1GLAJ PCIMGGU h1G2 O 5Q5 2Gc013q21 (PG GXbJUtOLA ALpJG2
500 1JJG2 (PG HIG9U jG2G Gx.Gwc A1flG2 conjq botGutTJA pc woqccq pA rucjnqju OtGL
bsiqcnr (pG 3 111021 GXP.GWG q11L(1OU2 MGLG OP2GL/IGq 013 (p12 qUA (JIG J0IJG2t 0 MJIIC 12 JWO2(
jpuju1u qA JJJG JLJqA OfJOItJU jJJ1YJC2IAIU qA cxpJpitcq
ru cflAr(A
p3 M1JJ JJOM (12 tO cowbLc LG2IIJ(2 E11L(PGLWOLG (JIG 1j121 qw 2G1 C0U(1J2 qA2 riuonuqu2GCOU 2UJbJG 12 gbbL0XTIJJ(GJA (pG WOU(JJ O DGCGWPGL E21W(!lJ bLSUJG(GL2 OL (MO qr 2G(2
COU(1J1J J2000 0p2c1Jou2 jJJG JL2( 12 bbLOXJ1JJ1GJA ipe woulp o ocujpci uq (PG
qTJGLGIJ(JA L0W WLJCG( OLqGL2 E2(W!OU H2 bGh4OLUJGq Oh (MO 2fl 29131bjc2 0 (pG qi poobGh.rru rpc ojjo,tni qA 12 qcjccq JJJG GXGCn(IOU 0j,
punt OLGL M2 1101 rctcq 913A
(1L(J0U2 LC WC2u1LG 111 2GCOUV JJJG qcTLpou GtMGGU tpc CIO2G O (JIG W1.JCG( OUG CX 9iJq
(JJL0f1JJ )Uf11(LA JT 1G
GX9UJTUQ (G qnLt1OU2 PCIMQGU 2flCCG22JAG tI3U2COIJV JJJC2CJJJGLG SLG OIGL oooo tLS1J2CPOU2 O 2(OCJC OAGL (JIG 3 wou(pJA bcuoq o WO/CWPGL T0
LGL2 JcbOL2 uq Ofl0(c2 CL0L{O)
qw
cowbjcq pA ocj H2PLOflCJC 91J IpC 4J2E
2(OCJC 1JJLOflP (PG couopqtcq (LIJ2C(JOIJ 2A2(GW JJJG2G qw MGLG 2(LC(G(J ow rpc gq2e JJJQ qt GX1JJ11JGc4 LQ (pG aqiu IJWG2e WG2flLG 711 2GCO1J2 1(GL uquipr O( [BV'
EOL mibj
).!' uq op (JgQ)
o, rp qA uq o oiput
UICL qA CJ9C12 qnww? UpJG M2
ncjnqcq£C!IJ rp AJTJG oIJ
!2 fpG rL21 OGUtJOIJC0uAGLr1J OL JGC UJbJ2 uq rp; Lf311Z bbc. Lfl21 lo impj in lwbo2cq J0 JJ0M 0L
woqcj rpc BHHH oqqJw it nq itirp unwcr.cj
JJJC O141PW Jrn2 130 £LOflJ2/L9J WOqCJa
21LIJtG
JIJ UJX!UJf1W PJ(C1p00q' 10 £IJG 13011 JTIJCUA oi rpci2j3C LG1J3T1fl AGLA pip LGJUAG £0 £pG CLI1JCJ AJnC
OL IJJQ rL2f.qw 2G1 1GL bL1WJTU 0(31 1G £JUJC Of qA J.GCrV pi POIJJ Ffl11-B0X
OL LpC rL2f qi 2t IJq J JQ 0L pG ccouq qw 2C( JJJG FflhJ-B0X rpc cuwjjA rnci.cq
combcq £0 j w p couq jp IJM r1nu-Box nrc 220C11J1 I#41 (PC CL!C 2 J5J
2 CxbCciq rp
qr (coiunrn (pc OrnpCL2) p jnpi ruqiq qGAJriou 0 J
mpGi. i(s) 12 u wuirc o
BOhr (PC 13CM 2CLC2pic wcu o bbLoxmJ1cJA j.
=
/J1c2pjj COJJ2IqCL woqcpu (pC hI$1J20uJJCq cu
UJ0LUJ1J £0 iJ021 90 2CCOLJC}2 LO11IJ 130011'
jou
rn qc wouirn pi bwcni £C ACLC qrn ou LUC2 jL0W TO 2CCOU2 13 tJC
wqqj
o
(C qA qrnu w £Q wowiu uq £C cuq o JC £L&1U qA ps
IC2 £MCG 2
1fl21 jci obCuru 1Jq Th21 bLIOL 10 CIO2C' JuG qnL(ou2 LG
9 PUJC2 J01JGL 013 A1.G 1J £JJG2rlp wbjc
bLC2GUIGq ! J1.G 2' D(1I21!OU2 LC J01JG21 113 IJJG iiiqqjc 0 (JIG qA uq 2JIOLIGL qUA' EOL pOIJJ qt 2G12 (JIG thrruc GP!P!12 (JJG GxbCcIGq JUACL1G fl1 2pbG' JJJC Lbp2 0L cp jjJCC G(CLI1fl1fl21J cowboucub2 MGLG bL11JGq Ofit (12I1J 1JGL 2bJTIJG 92 !1UC1!0U 0 (J1IJC 0LLC2CUICq u jtiLC 9' JJJG UJC9u fTLhiU 12 1)1CC 2 pp i UJq q £P9TJ £JJ1 0 (JIG W0L1J1J'
buor. 10 CJ02C' JJJT2 C9'U C 2GCU P (JIG ii.X qici.ui UJCU2 0L qlIjGl.Guf JIOITL2 0 (JIG qA JJJG2C 291JJbJC2 GXp!p!1 (JIG MCII JCIJOMII bLobA 0 JJJJ C(J/A 1J (JIG W0L1JTJ 913 1(121
.1boM
(UDA3)
UDA
thiinrioqx
di
lo
noiirrIli23
1.ô
brie2borIq
Iqrn
thod
iol
i&nui
.(I,1)QDA
di
asw
biirnsx
Ibom
1Iqmi2
cIT
£
iol
.r311
ith
1iru
IEfl
1rI3iknr2
£
2i5IrfI'
.ô 5ILIi1 iiibJa5xq
is
2ihJI
rLi
2lthom
riioa
.
I
>
(
+
x)
noiibno3
th
-thip.-i
I
£rrffnI
32c
o
nsm
Isnobibno3rw
irLno3
bn
if1
r1i
iol
Q8Q
brr.s0QQ.
o
1sup
bns
D fflU2di
rLilwbiiirii
n1d
oi
32013 biEhJ3J.B3 231qmS2owi
3111iol
2IIB3ffl LGrlOIlibnO3tlIJ b3ilqmi 3clT.13viJ33q-1
Lqrns
brxoc
ii1
rbum
31Eu1sv
rfi
bthoH
.'13viJqa5I
11.1bas
08.1
51BJ
£lTIrrl3Ilo
231u251rn2IJ
J3boffl
11i
lo
ifl
3±
3111msx3 i11rru1oT
.noi1E3i1bq25fl3
l3bnu
I
lo
3uIv
b
333qx3dJ
nsrü
aii
bthisbns32
31113fiSX3
3w
(&.)
d
b1uor1j3
3113 anoi1sv132doasq
no
bn3q3b
3onob
3
lo
noiiudhth
3113u3H
.53n.En5vbits
nsm
3113 ,IsinI3rloqx3linu
£
asbiudhieth
213
au3d
lorrrI3drwI
in3brl3q3brli
xoH-nu[J
3±
ii
wn
ifi
lo
3Dn3bn3q3b Is1oqrr13r13ni 31(3nirrrsx
oT
.13d
bluorla3
lo
13dm31r151)lo
3its
xoa-ruijJ
£ asri3Lqrna
izifl
3111' .b3nirrlsx3asw
I
ioI
313211532 asrl3lqmsa
bno332 3dT.
is 3u[Svth3ith
3±
3Iduob 21rbirfw
(
is
QQ.
21uthv
Lsiih3
3111 Hun 3d3bits
is
3uIsvIs1th3
3±
nsrfi1
Lizs3
EiahiT
..VI
lo
3iJthsi
xofl-wjJ
S 3(13th
b32w32ib12uoiv31q
2i13uo
di
isth
1li1
2131.b3rnL5I
ion
aiaion
iiñw
lo
23f11oqr1
.m3ldrnqnu13bom
iLufflib
5IorrIs
boq
3vSrf 31q1n52 WIll 3(11iol
E.
1 21rloiisiv3b
bisbnsia
dT
.1 21 j3 1onsrn
rf3
mth
1qmi
2nolithno3
bio
iaiil
ii
.llundl
i-i
'Iias
noial3qzib
X3
tol
2123T .31qm52 bno332 3113tol
Ô.I
bits
3lqtrIB2iaiil
nh3ffI3fI3gsisb
3±
lo
noirnln325Iq5Iboos
£3bivolq
111w I3borrl 21(13isth
'bti1
Ion
3to133th
21 .22330tqDA
3di
b n012t3V 3Iqmia (I3V £iaii1
.lnioq
21111 35riwsib
3dvsm
2n012u13no3owT
-nuLJ
3(11 ,31qm52 bno332cli
to1
.sisb
fb
n
2r10il513T1o3oiU5 b3vl32do3IJJqs3
ol
31dB 2i 131)01(1 3(11wol3d
'[2E3
213v31 01 3u1sv 15313h33±
lo
2233X3 fluisi
213v31moil
bo3ub3t
21 311211532xoH
2n0051v3bbtsbnss2
3tsL
bits
2(163(11LsnoJbno3nu
b3ilqrrlits1
dj
,bnoD3
.
is
3131EvIs3Iirr)
3ts1
3(13ioI
3(1130335ol
31dsion
21(I,I)UDAH
3±
Isth
323u2
23h32b3ib15bnsj2
3(11ni
.11w as bnimcx3d
1ias
bluoD 2fl011)t1251ibio
ifiH
J9T
i pdnuqA rpc jou rpc opucq qriipou o uo
rpc JG22 rjcj? gaq
rjj OCCJL gqirupnpoij
()=j) ia rj? Lciccicq OL poip qw cz .A<j mJbpc2 rpt rpc p&i.q 2 GCL9VU IIJ
O OOO?O q Ooo HCUCG IJJG
UflilpThOrJJG2J2 o couquJousj xbouijjgj
1J!TCW
i
ipc
2 cwq ro p uc OL porp qt uq ocirq ruqq
JJJG
L2flJ2
O fJJC /AVCD(PJ) oi. poip u3bJc2 i.c bi.cuicq m
yfl r-Luo2
Q Ef!W1!OU O,
MG!PflhJ VCD (JAVCD) joqç
uOt p COU2WU JJJT2 !2 BLGCI2GJX MPC '
mq
MpCIJ 1pC /AVCD UJOqCJ !2 GIJJtqOUG up cxbQcr pt tpc btopprjuk o iiqc
i coucproucq ou uo pq; rib o rnjj r um?
bLWIGL w IG q2P4prJOu Xicq2 rp MGfl Jcuottii bLobcu? o couriu bLoboI.riouJ pi.q
tp xboucutij 12
iciA acwpjc woqj 2bcrUcriou pril ii jo AD !uTJGxipJ lpc 2J1JJG
iiioqcj qoc uor jOOj( JTJ(C ooq cuqiqr OL Ip qw cUGLt1U bLOCG22 y2 wGIuouGq poL
EVCD woqj
cbpj o cbwi.u rp rnrucwboLJ COLLJUOIJ2 rpa
rn pob o inu pGrL it o it conjq u) u jwriic woqcj 2bcijcou
wJJ rnqicc booi. woqcj 2bcrUcrJou c conjq cxbuq rJJ woqj fUJJL OL (JJC 12 qr 2t
1P
H0/CAGL rJJ LGWT1THJ CXCG22 q BGL2IOIJ uq rp ji nubjicq rrncouqrnoirncouq jp v,o qqcq irujia pc pbcq ccorrn OL flJG rn ucwboL-J COLLpOu2 op2Ltq pJ
rpG cI4i3cJruq.q 'ro o C! 12 J4 0L tpC LTL2f q 2C 9IJq
J5Q OL IJJCLthcpAcJ? .LPG u'r !2 AcL) cjoa ro
ctiic ijn
uq rp ccouq i caijA jc rjrnu
pc r1nu-Box rc aocirq itup rp IMO uouiJcq 2GU2 91
9IJq1.
JJ J OL fQ 1JL21 9uq couq 2aubJ2 Lc GcaA1X jpc wbpq r1ucouqwoiJj wU2 i.wij ici.A
r vu porp woqcj2 c cjoc ro pru rn
jp iwbpcq nucouqurou-j wu
JJJC 2r1W O IpC ct uq 12 O? OL tpG QL2 gw 2Cr uq Q tOL (pG 2GCOU qr
jpQ iqA Lqnccq r-LrIo2
bLopp gric ro wn co ucrirA wou rp cxbiistoi)
2!1JjUC1U ( (JiG JGAGJ OL (G L21 2UJbJG uq SJJ pn( 9LC 2!IJT1JC1J( OL (JIG 2GCOiJ 2IJJbJG
JG2flJ(2 OL (pG EVCD(5) LG bIG2CIUGq J1J IJ1JLG 1JJ O (JIG JlJcJrIqGq A914JG2 1G rp bo22Jprp(X 911 EVCD(53) M92 C2(JuJ9(Cg
rnocoacjiou oi. ciipc qr r rporip qJc woqeja tcqncc ipe cxcc22 q2bco13e Mc
accouq wbjc r pip cuonp OLCL JAVCD 12 cbpjc o cconurju OL (PC
bLobou!ouJ ps91.q !2 1301 sbbLobuc OL rp qr v RhVcD(JJ) 12 S ooq CpOJCC OL [pG
..LPG EVCD !2 9p!c ro cbrnic rpc rn .[CwboL91 Couc !ou2 piir [PC LC2[Lc(AC COU2[D[ OAGL IpG MVCD(JI)
LCqrlccq
2[LI211C TOL [PC U12[ wbi LPC bWCD(5) woqc oci. rqc !uJbLoAcuJcu[
(PG pop 2UJbJG2 JJJG 13GM rii'-Bo 2t[!2(C2 VQ q wor R!(P [G cxccbqoii o rp
ccouq qsw cr Lc2bCcrJAcJ? yjrponp LGqflcGq MC WJJ uq cqGiJcc o cxcc2 q2bcL2Ou OL
JJ3c LC2flJtJ 2[SUqSlq qcrou O (JJC 13CM E 2CL!G2 FOQ uq FO tOL (JiG 1JL2( siiq (JiG U11 qsrs 2G( sug VU? 0L (JiG 2GCOUq
oooo o1. ipe irii suq ccouq qr LbCcp/cJ? jpc rubpcq
(flJCOUT1JOUSJWG1J J J 0L
LS(J02 pSAC pccii LCqrJcCq qnC (0 (JJC IJJrIJ[ICOflJIJCSLILA jpc 211w o (X42 uq
'
uq
JJJC G211WtG2 OL [JiG /JvCD(35) woqeja SLC JU U11LG T2 OL [JiG EVCD W0GJ2 [pG (-sbbcsj.a (0 C S ooq CpOJCG OL (JiG 2GCOUq aSWbJG '
jus
woqc C2 UJSGq itsa [PC MvcD(sY
JAC!PflhT 2UJfl11OL jp12 12 U rWbLOACIJJCU[ OACL (JiG EVCD uioqcj 2bGCJCS(JOU 913q (}JI woqcj
ro j iiq ipc aIUqLq qGA1(JO1J2 LC CJO2C (0 [JiG GXbGC[Gq isjnc TJUqCL [JiG uhlfl
O
s couqrnousj
JJJC r1flU-BOX 212(JC AcL? 2wj [JiG IIJbpGq riucouqrnoiisj WGSU J2 scccbwpjX CJOaC
[JiG CUIJCSJ AJflC 9 [JiG ? JGACJ
BOX 2(1J2PC2 SLG
iiq JQJ jpC J1'-B° 2[(J2(JC I,OL [JiG 2CCOU aSUJLJC
sT. pqott
woqGJ2 p3 pOIJJ 21JJbJC2 MG 2[TJJ LC1CC[ rpc IJ11JJ O HO GXCC22 qrabcLaiow jyc saaocisicq
r1nu-MCijiiq [JiG awuqq qG/Js(Joua LC JCJQO uq j•() JJJ!2 J2 S LG[ JiuJbL0/CWCU[ OACL [JiG EVCD
(4)
E=-r)
[JiG MGIP11JJ
[JiG CrJCLSJ1cq CLLOL2 S22OCJ[Cq MJI}J (pG MCIPfIII woqcJ EX (JiG 2[S13ffLTC 2GLIC2 OI. acouq asuibjc psa ifli nUcouqrnoiJ9J WCU /GL) CJO2G [0 (JiG 2swbjc ASJflG O J JC LTCX[ CX9IJJJG qsw 2C1 12 sJUIO2[ J UWG2 MJi( it aponjq G q (PC woqcj MCLC COLLGC[J? abGClIjGq MpTJC (PC
OfI[J1C12 LCIJJSflJ S woqcjrn bLOpJGW OL [JiG (JL2[ qsis 2CV JJJG fJUCOUCJp3OU9J IJJGSIJ OL [PG U12(
uibpcq
mJcouqiuouSJ WGU 2 J OL (JiG 1JL2( qS(S 2Gte suq J •Ø3 0L (JiG 2CCOU fiG GGC[ 0,fl2J /AVCD(YJ) tG unjj pThorpr
GGCt2 OI'JI f12t 2 MG qiq OL IpG qnLrJOUv JJJG rcr MGLG bci.ouiq ou rpc 2GC0tJ qi cr
AOJflWG IJq bucc cpu cxpipir rwqi. qctcurnxn2nc cowbouGIJc Jy*1C
tJJCLGOLGbuJGq flJG2Q
AGLG
]flt
qic qrn.tiOu2 Gxplprtcq CtGU1JUJTtJC C0Wb0UGUi t2QpGq CL ip
uq rp bcLccIu 2bLcq J.cu rJ.ucuou coacbouq to JC2
UJIIJJtC2 oJ tLq1u oIJ
TUT0UJtJ0IJ LtJJGL91J AGLGbLOAIqG2 gPGUGLWG2fILC O ipc CfJLLCJJ( O AOJ(TWCe AOJUJTt
itiptcq J2 OL GC cua JJJG iqc 12 tp 21UJQ
ctiou OG2 not cu? wncp
MtJJ LG2bGCI to cp o ipc inpjcv JJfl2 M qoiic p? t9JcpJ woinJ sici.c oT, jO
jO
OUllfTJtG JC2G tQ2t2 MC tJl2t CLG1G 21IUUJL? 21tT2IJC2 ,OL tJJG 2t1G O1, tJJG IJJL1CC1jcq qra ov to tpc uJOq]
GJJGLJ !JfOLGLG22JAC 2bGCIIjCtiOIJ o itt !. y 21wbJG 9JiGWt1AC MoflJq G tO!uaoqncG
2dntc2 o
pA9u(To5) 0L B0JIGL2JCA uq DOw0M!t(Joa) VIJOIJJCL !UtLru IC2t uJipt pG O WOLC
sjc (rpc 2bLcq) MOfJJq 2O pG 1J JtGLQ2tIJ 1.pJG tO GXJUJTIJC 2 OL GXlJJb1G
W1G2 111 OLGJIJ GXCS1JC UJL1(Ct2 pAC 2flG2tG tJJttJJG TCLGUCG GtMGGU LJJG piq uq IJJG
AUjC2 I,.OW OflL nioqq 2bGCr1jCtiOU' P3 qqrnou 10 IJJQ2G JpJG2 2OWG LCCCIJI GWb1CJ
cx91.U1ucq jjiec
tpcoLGrJc9J woqje tpCLGOI.G 2flG2t OUJJf1J1!U 1C21 0L OUJ!22OU 0, (G2GC1JG2 IJq AOJTJWG JJJG U9TIILG 0 JJC COLLGJt10U 2 wpin0n2 qCbGIJqTU OIl tC WOqGJ
(iY iu bucnJL tG2G bbCL2 rpGoI.G cpc uo-aq qm.rou2 ponjq G coI.I.GtGq itirp bucC
p? iiiou OtpGL2e AJC(Jg qw uq GqGI.GL(gg) uq WOLG l.GCGUIJA' EIA uq OH91S
COaGJtiOn2 C1MCGU bucC CUG2 AOJflWCe iiq no-tL9qG qnLti0n2 JJ112 qc GGU GXUJ1JG hLOW IIJC L0MiIJ J!tCLLr1LG 21II.L01JIJq1U LIJ2COU2 qw OLJC
uJpt
CXbGCI to juqUfJII
LGLG2210U O AGCfOL O 011G2 OIl IJflWGLICJ CJJntJOU2 O IpC 2COLG ACCIOL CAIfl1GCJ 9 IJJG
PrIC I20 b022!PJG 0UJ12210U O C0i.JtG2 jpG fl 2ttJ2qC J2 G2!1A CCI1J1Gq 2 1*15 0 IPG
1G21 bLoJJqG2 2flJJbJG L91JJGMOLJ( 0L tG2L11J 1101 ouj? IJJG f]t0LGLC22i/G 2WICI(JLG 0, IIJC woqcj
2GCt0U /tJJJ bLoMqG 2OWC 2rWbJG GXWBJC2 O IJIC r'LIJQ flJLJbflGL 1C21 0L IJJC VCD ..UP r'
!U2!P1 !IJt0 JJOM UJ1JCCt2 MOLJC 1Jq GAOJAC JJJG tOUJJCL M4JJ pG cxurniqJil LJJG UCXI 2GCtOIF JJJ!2
1M0 IIJJIIIGqIIC (12G2 O tJJG VCD woqGJ LC jOLGC2tJIJ 11U2C10U2 LtG2 iiq 1JJIJ
fl"I JJC2I2
uq fPC
01JqqOUJ DnL!0U oqcJ2
CC0r11J1 T,OL (pG q2bGL2JoIr
qniiou2 rori MC qtjucq qni.wou 9 qic t!wc pcvtccu tito ncccmc 11.SU2CL10U2 MC
v
OLMBl
MA to uaoqncc AOJflJJC TjQCt2 !U10 IPC VCD woqcj 2 10 LGqqJUC O(TL UJC2flLC O qnLUowitrjj &oboc u j ujgujc
woqcj2bciUcpou tpt ucOthoLtc2 IPC
O AOJFIWG 11310 IPGIIJC 210CJC WLj(CC tLIJ2CPOU2 qr !t !2 qJC &IIJ1UA o pi.ca u.qcq JJfl2 ccou oi, pc bbCL
2bCIJt u rpc
ucnoiY
rcjcbpouc csjj2 t wpt pc tpc um1111G2 2aoc1cq H1tp IJJC CH EOL
uouou ot dn9UIJA 22OCJtCq flp rpc O2GLitJO1T EOL CLCqt csiq bnLCJJ2C21 !C 2 Ipe OJl2
0L W02t O £pG CXWb1C2 o bLocc22c2 flJt UJAC t fliCflJL rntcLAp rpcc 12 2OWG
g u yjcuJuc oqcj bGcJcpou 0 PJ0C O11'Jt!O EUPCI2
PCLC PL!1J to uuq wuA Cipel. bo22ipc cxrC132!0U2 uq 1C212
C1MGC1J IG2G WLJCt A9T4pJC2 JJJC 2IuJbJC GX1C13210132 0 IJJC VCD woqcj 2bcC1UCt1OU2 cxuJucq
uq 2GACLJ OIPCL WC2f1LC2 O IJJG 211C o (JJQ U391JC1 flJ2
wipt
PC JUCUAC O COWOAGLIJCIJI!
pc u oAc12ruJbJTUcLJow JJJC2C (G2V2 bLoAJqc CMqCIJCCcoacjiou CtMCCU qcuou
2bLcq2 jpc jcq 2dnLcq qfu1J0U 12 ACLA 2UflJCflJt 2flC211J 1JJ1 IJJG JpJCL 2bCc!IjctJou o
JJJC flAt 1G212 21G2L tpt 20L1GL flLU0U2 OJJOM p1p AOJ rp1A jLC AO1flWC uq iic
X(j)=
r'y
-2wt2t!c
g.QJtT3?
QIO!I 21O!I
2bLcqWC2t1LC 12
wiiujj?
uot LGlccrcq"AOJtTJJA uq AOJfJIJJC C2rJ) LC1GCI IJJG U(IJJ p?borpcai 1JJ1 IJJC COCjCJCIfl2 LC SCL0 JJJG jcq
O wcqoui t IJJC
JCACJ 12 3 f'Cq 2dnlCq qra1Ou2 iiq IJJC UJC2FILC2 0 jcq
2dnLc O jcq uournpcq qrJLWOiJ2' JJJC CLJ11CJ /JflG OL cJIJ-2dn1cq 2tt!21JC MJIJJ J qCLCc
210! J tpQ uoLwJ
eqwoiu ACLC o tpc bcLccIu qIIJ4GLCUCQ 111 21( q pq uq X !2 Ipe
12 1}JC uowpcq UJOA1IJ ACLC O AOJ9ITJ1t? Io1 12
tG uouiijicq WOAJU ACLC O AOJflWCe
uqqriJjA CflILCUI AJflG2 O IJJC ASlJG2 MCLG not ncq qnc to ipe boteunj cuqoeucitk a°'
JiJe 0JJO/tJLJ WpC COIJWTIJ2 qc FN 21W2flC2 OL IJJQ 01131221013 0 ccp O IJJC A9UpJG2iUq1CtC2 tP1 tpC OP2GLAC C0LLCJ110U2 LG 1101 1fl(G1 qn to PL01CGU nb tLqC2
o cbrriuu tJJG 11J1GL1GWbOLJ COLLGJ11OIJ2 JJJG J'LG f110C0LLCJUOU2 111 IJJC AOJFflJJG qr f'LG J1tOCOLLGJWOU2 IC O2GLAC 13 pC A01J'IWC qnJ.&1ou qrT JJJC hWCD !2 cbpjc JJ2e PGGULCrJ? LcqnCcq 10 MCJJ CJOM luG CU11C1 A9JflC
tjrnu 0UG Jul12 M2 CXbCCICq qnG 10 tpG 2Wfl 02CLAC ALUCC JJJG r1nu-Box 2tt!2tC o,
P2C qrrwou WOCJ LC bLC2CUIGq Iii T1LC J J
JJJC cxboucut OU tpG /AC!Pc1II 2 UOM LC9TCLCCOT1U1 OL 1JJC JLC !tJtCI.ICWbOLB1 flt0COUCJ10U2 JG W2flJt2 T.OL 1C MVCD(5) AOJtIWC w0qGJ 2 UJLnJJIJA LG1CCIGq 111 AOL o tJJC MVCD LOL poqJ WOqCJ2 (53)
2
UGCG22LA top? (JJ2 LCt!01J JJJG 2tIJq1q qGA 11011 12 cu1ffJJA JC22 £JJ1J OUC UOM (
JJJGEVCD
21111 iLA 2i1JUjCU1 V2 OIJC W1pt CXbCC1 fiG atuqq CAWOU JJ2 PCGU LC11CC 2flp2L19J1? COLLGJ1J0U2 LG 211JJ ACL) W1.G IJJCf'lflhJ-B0X 2W1121!C
pCCU 2JprJA GCLC92C 10 J par !2
2 pGI0LC JJJG bLPJ
fltOCOLLCJ11OU COGUC1CIJr2 91C bLG2CUICq ru jrnG io JJJG rn1GucwboLJJJJC qGICLUJ 11 21K UUJG Oj qX CGCt2 MCLC 211fl bLG2CIJI 20 tG2G CCCL2 MCLC b1.qGq 0111
0000 Op2CL/t!O1J2e Q4
Op2GLAt1OU2LC GuGL1CqO!1GU fIG WX1WfJW AOJI'IWG op2CLAcq1 GLO 2CCO1J qrmf 0112 MGLC 21JJ bLG2GUI hLOUJ fIG 0LIJ9J
O000 21JLC2 10 GIjUC qrn.aou JJJJ2 iuibjicq
u AGLC
o1n2r OACL JO tLC2 bGL qrnsriou. JJJC 113 UTUJTJUJ UFIWPCL O 2JJLG2 rqcq M2 100 tq fIG WJXflllflWM2
J0oo MC CPO2G
JJJG ACLC AOJ1IWC tLqCq OACL O1JJ 2wbJc2 12Mi1J1 21UL qGMr1ou O 4JJ
2LG2 L1JJCL qJu fIG LL!A9T O rLqcL22UJJJCL OUC2 CXCCIItCq OAGL 20LL 11111G OLC 11JOLUJ11OIJ uiipt J)C COUt1UG 113 fIG UOM O,
qrs 2C12 12 10 1Jibpcq? CCOr1U1 tOL JLG tLJ2Ct10IJ2 tpt AC CC1J L0JCGU rib
JUIO 2CACL9JUO1CL LG2OU MG uiipt M2IJI 10 JJOM 0L AOJfflJJG CC12 MGU GX9UJTU1U fIG IJ91JC1S1
P2C qmqou2
O U1AJ O rLqGL2 JJJCLCOLCe ru C&UCX UJ14(C12 1 bL11CfJ14? 1J1G1C2PIJ 0 CXU5UG /0j1TWC fIG UOfOU O fIG L1G t MIJTCP 2}JLc2 91.G tLG 12 WOW WG91311J.pJJ WG2IUG 1JJIJ fIG L1G
yjrjonp fIG
uoqouo
pdcnqrA 12 UOfcwj?. qrucq 2CC BJcJ(J iY
11 iionjq2CCW JfcCJ? uoqcj 0 fIG UOM O 2pW2 L1JJGL 1p2IJ fIG LG O U4AJ 0 tLqCL2o rpc nucouquouj rwbjicq
wu
uq rp ouc 21Gb oLcr jjjiu cx+ 12 cjo w
ouca MJJICbncnjr
OL vcDU j) rp oz.ccr o ipc cxbcccq qnqou wbA
,tptq
AGLC
Jill2
LCbLG2CIJWflOU bLOMqG2 2OIJJG W2Jp1 10 IJJG bLObGUG2 o 1G jc-etcbOLCCr
p
(t) x =
(J—(c+t),1)h+(c1+
b)*t'
np2pnm iu r 2rwbJrIjca rpc GxbL2iou o
()
X
E E(x) =
(x+
1
p1
b 11C11L 1G I 21 IOLGC21 OL 1G VCD(TeJ) wj 2!LJJbJG 0LW O
()
E(X(°a) = '
+
Z&E(x' )+ V'E(IKI)
IOLCC21 IOL
VCD(bad) cu G rtcq LccnT2!AG1? s ojjoit
HGUCQ /K!41 !2 1G ouc 21Gb qnqou OLGC21 9 ITUIG a uq r Mifi G qcuorcq pA x jjic
Jc-2rGb(4?) E(X'I)
= iK' = ii' +
+ ZA.M
VCD(Bd)
LJG2 IJJG OLW OJuq ujnjtr
21GbLCCI212 OL rp 'lCD uJoqcJ r2 uotcq U 2GCI!OU J IJJG OIJG 21Gb OLCC2t OL IJIGcxuibjc !t !2 rile rnjjc pcuccu
2rocjc rLU2CtJou2 jJII2 2ccrjoU injjqcwouarc
ouc rcb
LP 'lCD UJCJ2 I)LOATqG LWGMOLj( OL OLGC921!U IJJG{3IJJC GtMGGIJ J1U1LC CAGUC2e U OIILJJJ2 2GC4OU Mifi l2Cfl22 OLGC211IJ tLqIJ L1G2 1J2IJ pG EVCD iq Ipe MYCD woqGj
LLJAJ jnp (qnLqou2 LG 2pou) uq JOM criqD i, rp rc o
io (qnLr1ou2 lc
tMO 2CGIJIJO pip uq
9U4A9J L1G h
M1JJ1 P9 PTP 1!'!O r rp irc
ipc rob o
j bLC2GUr2 rpc wnj-b OLC2f2 o x 9L fG MVCD woqj nuqL
ponr
rp cxbccrcq ijnc couqrnouq ou rui o qA uq rp ppr w uct qonpj
tOLCf OJ C' ra 2rJperurwJJ? wow ipjc rpi rp qcrLw11n2PC bw JJJ JOMG2t OLCC2 LC
qcrcLwnm2uc 2bpuQ uq rp oIJc-2rb owcr jr bbui ow rp ibp rpr qi ou 2b
rp couq 2uJbJc jG qorrq jmc i opcucq qrniou jp ro opq JTU2 ic rp
E!nL j bw2GIu
rpcou 2rb ocr o rp MVCD(rT) woqj OL 91J Lp LSL? qu? u
(i) E(1I)(i
HCUC IJJG OIJQ 21gb oi.cr x' 12
(o)
Ecfre )E((rt)J!)
Mp!cpe pA iuqcbuqcuc i
(t) E(XI0a)
=
JOC22
O X1 LGdIITLG ijnwou o rp qruinxJJ2uc cowbouGur J.pr
tG 2ccouq q
tJJG occr 0LOU mCLg2c2 hO1.GC2r2 /tJJJ LJJLGOLC pG BLG2GIJLGq OL 1pC /AVCD(L'J) riu
oLCc92rju bLobGurG2 pi buicriji.e rpC OLGC2t ij uor cOuAGLC ro 1G nucouqrnouj wcu g
Qdnr!ou ()
MG2CC rpre tOL rpC qr usJACqe rp EVCD WOCj2 MTfl AC fmqC2ILpJC
jpc mJbJJGqWCLJ2
1C wncp JLGL ip1J rp O2CLAG wcu OL rpc EVCD woqGJ2 ELOW
wCU OL wuA ercb2 pcq
rp qrmspou2 p iicu aqa OL rpJ2 bucnj cr itqj pG
pA rpc fTLLCIJt COIJqOIJJ crjurnrc bcIoz.wQq !U qir bbcL 21w £0 CJO2G ro ouc 91Tq £GLCOLC Jc-2iCb OLCC922 O, £JJC o1.cc2r JO1JCL /JJJCIJ ct+ 12 2WJJ rpc OLGC22 MflJ dcJcJqA LCrrJw ro rpc rmcouqrnoujtpG rntci..rcwboj coujnou ipc ji mJbJiGq
wcu
uq fG ji wuqmqiscq 2cuq.q
2LJqlqrq 2u2 jjnjc tG GxbouGupJ /2JOU O rpc VCD woq ! cbpjc O CCOnuu OL
ni flJ op2GLAGq uo-tLqc qrn.riou to ijnc JG2 191J (JiG C4tCJ AffJflG O 5f OL VG
IOLWflJ1TO1J /tG1.G 2flCCG21JJ Hi 1GqnciL) GxC aiA 2rtflC2 O MGJJ OAGL 1000
EOL p iiJnCisj tLH1JCnoIJ qw ncq ru qn bbG1. it it 2poMu rpi ici.? 2uJbJc woqj
UJLJCG1
qw ncq pi rp bbGr r 2Gt qiG rucJnJou o OtJiGL wrn.c o,
rtc o, n
woq i rjA uGt.Jrsq to rncjriqG oipcL xocuon upjc uq OL tJiQ U9UCJJ 1J2C1!OU
C(T2G2 oj rrw qouJrntiou mnG
12 woqcjcq qmccq? g iJ fl1OLGLG22!AC bLOCG22 JJJGJ(PGL (pJ LGJkIu ou IJ G)COuOr12 upjc to qui flinG qcJoLwtJou 0!. nwbrou2 ou tG
JJfl2 bbcL p utoqncq g woqj oL gw tJi9 qo uot uic t LGflJL tUJG
J0 COUC1J2!OU2\D!Cn22OU
(rinG OL Gt IJflWGL O GAGUt2 u JJJG tob O U(JLG J WG2flLG2 IG LG 0 tLiJ2CflOIJ
nucouqrnouj wcu s opcuq iii cdnwou (g) jp pouow o rn j oI.Gct ip GxbccIGq
TOLGC2(2 NJJJ pCCOwG bi.jcj (JiG 1OLCC2t JJOLIOU !1JCLC2C2 JJJG 210bC M1]J coUAGLG £0 tJJG
GUGLtC ph tpc VCD
cxbccrGqe uou-jrnl r.qjcctni rpc qcbGuqGucG U nit1OU2 JJJG2G
JJJG2G OLGC2t2 SLG 1JJOOfl2 £0 £JJ cxubjc pi fpC pouow o IjflLC j jj 2GG rpr iJiG OLGC2L JJJG pOUOi.u O IjfTLG J bLG2ur2 (G2G IOLCC2f2 tO!. (JiG 2911JG (MO ,JJ1JJ11 1JOM 2CGL02
() E(t) —
= E[ZX+
J
= E(XJ)
G2Jh cjcnjtq ph
yii JtGWTJAG tOLGC2( ot fiG CXbGCrGq UJC I1IJ(T J( iJCrTOIJ2 (CG bJCG JJJ]2 12
(JiG 2f1W O fiG (X2 uq 12 UG. OUG IJiG 1OLGC2i2 COImGLG 2JOMJh to rp nucouqfoIJJ wir
rnicouqwouj
I.G qm.roir jpcX ac 2hUJUJGPJC pOnt tpc fmcouqqoIJffJ WG1J o j BGCn2G
crrric I.GbT.G2GU2 fiG jqp cuiih wnJtr-2tGb tLCS2t MJiGXJ cnuGur qmnou pcni t
(JiG MJJGIJ CTJLLGIJI qrJLtiou2 pG1IJ ( J £IIJJC2 (JiG flUCOUiPOU9J VGLG qr1Lnow jJJG jOMGL COUCAG qrrwuou G(MGGU aqG2 JJJC flbbGL COIJAGX CflLAG LCbLGU(2 (JiG JOM CUA1(h WflJU-2(Gb tOLCC2(woqGj
woqj ionjq lorutjA uioqGj JJ IJJG2G LJP1G2 bCLPb2 (p12 12 (JiG W021 rnrcLG2qu CXIGU2JOIJ 0 (JiG 2bLGq21 bucc2 fOJflWG siiq qnLiou2 LQ woA!u tOCtJiGL £JJGU
UU1L CuGLpsi0u O (jiG
1G(2 rnq1crGq JJg (JJGLG LG 2GAGLJ OIJJGL A91JJG2 (P( conjq jiVG CU(CLGq OfIL WOcJGf
II
CJGI.IA (JiGLG LG IJFJWGLOfl2 GuGLJ1110IJ2 0J (JiG woqGj (Ji( COWG (0 WTIJCJ JJJG
cxbGCrnJoue G OJJOMGq pA 2rJ2tflJGq p1p (joii) CtTA1A
LG(m.u to (JiG rwcouqrnouj WGU AGLA LbiqJA y bci.oq o, 2flUG pp (joii) gcjirA ,tsJr iii
couqrpouj UJGIJ GxplpJGq 2i1JrIjC1J( A0(JJJ1A JJJC UJfljJ-2tGb 0LGC2(2 O qriL ou qq uot
EOLGC2(7 MGLG qGAGJobGq tOL Gxbcc(Gq qnLfou2
JJJG OUC-2(Cb 0LGC2(2 0 (pG
G)CJJipJ(2 JLG JU(GL(GLLJb0LJ OCOLLGJUOU2 rJrn MGLG 2rJCCG22JrJJJA woqcjq pA
iq OLGC91JU pdniqirA JJJG LLJOflU( 0 (puG IJCCG22LA 0L 50e000 2P1G2 (0 (CC bc 2t11J
UJAJ O tLqGL2 hOL J1JUC1 rLU2C1JOU qw 1JJ!2 UJJJ( bLo1qc pG(ICL MA oj wm.ju
JJJ12 bLoAJqGq (JiG !u(GthLG(1!0u 0( wOqGpu (pG LLG (JJt 2jJLG2 1G aqcq L(JJGL (pU (JiG L9IG oqf1LP01J2 EOL (pG JiIJCIJ qI Gt MG (12G (JiG IUJQ OL 2G( IJJ1 WpCL 0 2JiLG2 (0 pc tqGq
vu GLIi(T/.G flG 0 (JiG t9 0MGq i'm to 220C(G S WGS2fTLG O dn IJVA M(p (JiG
AOJrIWGe suq 2bLGSq
JLGL 2bLGSq2 JJJGG 1G(2 r1GC (JiG bo22!prpLA 0 COWOAGWGIJI G1JtGGU qrn.SrJou2 AojsupXa
mqicS(Qq tpS( 2J30L(GL qnLsriOu2 0JJOM bGuoq2 o, pip Ao rpiA JSLG A0Jl'IWG bGL tL1J2SCt!OUa 5jJq 0L jSGq 2dnT.Gq flLSUOU2 2flG2(G (JiS( IJJOLC COUJbJGX WOGJ2 UJipt pG cou2JqGLGq JJJG LG2(2 qJI,JGLGUCG G(MGGIJ piq suq S2 M WSLnJflX UOt LG1•GCGq JJJG LGGCt1OU O (JiG UIIJJ JJThO(}3G2!2
OUJU(Gq WGS2TJLG2 0 JSGq AOJFJWG iiq AOJStTJJ(A G9'211JA LG1GCrGq (JiG ur1jj pAbolpG2i2 jJiQ BGLCGU
'A1 (G2(2 bLoAGq to p 2rwbJG suq A'J(1SpJG 0L (JiG qsr SuSjAGq JJJG (G212 JOL
qoc s ooq lop o woqjni OL (JiG ccouq 29uJbJG
ooq uuoqcj CPOICG 0L (P!2 qsr P bSI.1JCAJL
2PIJbJG 2COU °T hWCD(Ji)
mucouquiousj WG91J (0 ASJf1G WflCJJ CJOGL (0 (JiG 02GLAG IJJG9LJ JjiG /AVCD SbbGSl2 (0 pG 5 GXbOUGU(JSJ 522r1wbn0u (0 5 qGCLGs2ru pssLq JJJG MC!PnJT qi2aJpflPou SJ20 LGfJCG2 (pG rwbpq bST.SLuGIGI. 0 (JiG MGipnfl 12 AGLA 2iIJJUCS1u stig C51JG2 (JiG COU2ISIJI psssq ruJbpGq pA (JiG
qGAISP0IJ2 (0 ASJflG2 AGLA CJO2C (0 (JJO2G rIJJbJiGq flIJGL COLLGC( wOqGJ 2bGCIUCSL!0U JJJG sqqousj
(IL(JJGL flJJbLOAG2 (JiG rlnu-Box 2Wt1213C 0L (JiG 2t UqLCJTGq qflLSflOU2 9'uq LGflCC2 (pG 2WU5L
GX(GU2!OU L0UJ (jiG C0U1(J0U5J GxboucliusJ q2vL1pflDOu o qni.spou to (pG JACipflfl (p2fll0U qGAJSUOU2 iwbjA (pS( (JiG COU1tJ0IJSJ GxbouGu(1SJ S22flWbfIoU wA uoi PC S ooq 0uG 2fluJbJG
qrn.ou TLc1 itc qo nor 1c1Jo/t o uA bbJJctou2 ro 2OCJJ2t!C9JJA rp.u ii.Arn piq
ro cou2iqcL 2cun-bluJaJc c2rnJJ1Ou bLoccqrn jjJrj rpc wcrpoqe ic /cLA cowwou ru rpc
qw wpGu iioqau MIfJJ pc rL9ucuou2 qr9 pGuc lrnwL9J xuou oj tpc woqcj ionjq pc
couiuur bLobi.O rp woq conjq
p wI22bcrrq
In u12J pic prrnqm.rt
'4
'4
JJf1LG J. CO1U1!U bLOCG
V (i)
w(r)
0 0 Dfl191!OtJ
100
300
300
400
200
I
3 3 4 2a
aI0
II
1313
14
12
1€
0 DflL94!OU 100500
300
400 200 0-J 15.
3 4a.
.10
11 13 1314.
12.
r'1nu-Box(T) =
r1nu-Box(J)
=
J
U
OO
N
013 .O8oOJ
J J3
03ô
030
J J
03ô
J JJ
053
JO
OT
J JO
O4
.OJ
•O3
OTJJ8
0tQ
05J
0ôô
.OI
.OT
053
100J Q
OQ
OQ
OQ
.TO
0Q8.og
0Q8Oft
10Q 081.OO
0Q4J50
10QJ T
•JQgI8
JÔ
J5
bc
bc
2bJCI
2UJbI
5xg
3-3
513X5o•J3
1-33itQ
13-1Tg
35•!t
J1-J3
5338 3•38 10-IJ53Q
3•53 31R0HOTU 1AI91J
eq.
2uJbJc
3
3QJ3 3'4•1 34•T5 3-3330
5•Q3
J5
TQ3
330Q5.1Q
13-I
138
3318 J1-J3 33Q0303
JOFO 10-IJ 5503 330ô ô:30-J010
Jfl.X503
HOflLE1.d
2SUJbJCj
hJ11LGI
I.1J DIWfl!OU pA HO
10 11
IIWG ot DSX
iS
13JJWG O DsA 13 13
L111LG 2 IGTJ couqqoucq
OIl UIJJG O DA
a 10 12 10 50 30 20 0 10
:
30 a 12uciqAqnwuxA
.Ot
0) OJTQOOJJ
CWC!GI.It 2rq ELLOL2uJbJc
J
qr'uiwA •JJto lJ.ooo
cxJ3J
0)OOJ3
OOOQ8X T03Q 2tT ELLOL2uJbJC j
JJITJJCO
D
EUCCI21.1GM qA
qnwm?
.oo
-1U
J8
FOQ33
oJ
-3fO cxl.O.o
OOQ4
C') OO85.OO52
COW!G!JC2q
2urbJQ
.O8'&Xcx
-I3O
cxlOO3l
000QOJ C0GWC!C1J2q
EI.L0Lmbjc
j
JJLIJC O D'
E1CC
I-I°: )=j
ucMqqnuJw?
-oi
8110
-3F8Q
00438T5Q3
aT
.OoT
JQ•o
C') 0TJ3 OOJ2QCOUIJ1
2q
-B'flO
21Ub!C
uqqnurinA
80Tô OOQOtT
OO33
MÔ3
aJ
(T) OOOQ CO.UC!GIU2q ELOL
211JJbIG JJJIJJG O DA EICC
0
*H :=j
ucMqqnwwA
-33
JJ3J5gjj
OO2ôI3J8I
QQ3
JIQQ3QtI
JIO5
J5OQ
88
-.oto
00?303ôO
C') O3OX 003JJ3COCU2C!GUr 2iq ELOL
t-JU0
mbj
13CM qA qrninn?-33Q
8OO
OOQ3
-313
J5QO
-13
-O83ô
OJ32
.TOo
OO83
JV82
C') OOfOQ OOILXQRÔ
COWC!
2T ELLOLt-JJ0
wbJG I
JJUJCO
D'
ET1CC
r1nu-Box(u) =
i
u
103 0T81J3
OJ8
1 13
Jt3
i is
.oo
JJJ
10.X033
JJo
.1J
O3
J8
13
O8
JSJ
05Q1Q
.OôO J33 02TJ4
TJ
OQ
J3
183JJO
J3
J I
585
585
bct
BOW 2uJbJc2
0
*H :)=juMqAqnarw?
•J1Q
5088
0JL13-m
-i
IJJ.JJ
•JO?Q 8RXt cr3O3't
cxl8TO
0) .OTOO 300J COUC!I1t 21q E1OLnoisiua
L) CAH
0
0
0
0
•0
I •0
I •0
-0)
-- ----'__
_____--
-• — — = ________
--
•;__1;_ — --
'-4 '-4H
— —•b —
— (.4
- ---."__;_;_.•
-E
---.=.
C) •- _______
__-jr
ass-_____--
____
--7--•-
'—1--
___
• - --F
_
___
-
--
—- -
H
- —-.——--——-.-'.-- .-_________ - --— -—
•::;g
(0H
LOLGC2
OL JpC MVCD(rT) oqc
J
.
J..
J •ç;fl4nIe
iauaCpOu2
— — — ———————
1
C.1 C,1 CA CeI —()
4
rOO
kU
C)-
CA C)4
rOO
I—O
0
-
CA c..)4
0
F',x
co
0120
005
m0'9
2
0
Cauq
rOM.
CflLLGUI DflLOI!OUceuaLIo2
oleco2eq
cnwnfoe
iiwe
to
kfltflLG ILOU2OCBOU2 tOlH!ap.
kfl4ILG 1L0U20C4!oU2 CA CA CA (A C'l — CA C)4
rOO
-
O
C)-
CA)
4
rTJO
L-0'
0
CA4
ceuaqo
oLeca2Ieq
DflLOHOU2tOl
.H!alJ.
auq
.roM.
CflLLGUIjLOG
BOtGh!"
TT
AIflJf!-2Cb
EOLCC2JIJ
nr'
W
MVCD(TT)
oqcj
E(J1! —I'T) =cE(x —ii) +(x+b)5E(Ih' —IT)
=cL(x'
_JK!_r)+(cx+)(Jft!_I
._h)sK —tc = c(xHI —T)+(iK —
iK' =o+cxx1 +it'
bL00.
O F'cWW
JJJG couqjrwu pt
(&
+
<j IJCCG22L) tOL jj
rp
L0012 to p ont2iqc tp nun crLcjcOED
H— 1
j(! +)
II g
tQ LOOL OT, tp!2 qLIJCG Gdcrnrrou p Onrq IJJG JflJJL CLCJG qJU=
cT--(&
÷!)i-20 OL1>be
÷(!
+i)bi4I
=
o +&E(x
)÷" +E(x!_bI_b_1)÷
E(JK
1J_b_1)+. ÷bE(Jh,_bI_b_r)E$JUG S =
jpu
ijcru Gxbcwtou2
S' MLT
jjtpont JO2 o cucLJuA b=d
bLOOT O f'UJTJJ J