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BQ. 1. Jnembn rnsnari` Ont`cjckchy. Nxpkamb t`n oagcr icopcbnbt ce rnsnari` ont`cjckchy. X`at arn t`n

prcinjurak abj prcinjurak pnrspnitmvns ce ont`cjckchy3Abs. Z`n Vnsnari` Ont`cjckchy ms t`n prcinss usnj tc ickknit mbecroatmcb abj jata ecr t`n purpcsn ce oalmbh

fusmbnss jnimsmcbs. Z`n ont`cjckchy oay mbikujn pufkmiatmcb rnsnari`, mbtnrvmnws, survnys abj ct`nr rnsnari` tni`-

bmquns, abj icukj mbikujn fct` prnsnbt abj `mstcrmiak mbecroatmcb.

Vnsnari` ont`cjckchmns iab fn quabtmtatmvn (ecr nxaopkn, onasurmbh t`n buofnr ce tmons sconcbn jcns scont`mbh

ubjnr inrtamb icbjmtmcbs) cr quakmtatmvn (ecr nxaopkn, aslmbh pncpkn `cw t`ny ennk afcut a inrtamb smtuatmcb). Mjnakky,

icoprn`nbsmvn rnsnari` s`cukj try tc mbicrpcratn fct` quakmtatmvn abj quabtmtatmvn ont`cjckchmns fut t`ms ms bct akways

pcssmfkn, usuakky jun tc tmon abj embabimak icbstrambts. Vnsnari` ont`cjckchmns arn hnbnrakky usnj mb aiajnomi rnsnari`

tc tnst ypct`nsns cr t`ncrmns. A hccj jnsmhb s`cukj nbsurn t`n rnsnari` ms vakmj, m.n. Mt iknarky tnsts t`n ypct`nsms abj bct

nxtrabncus varmafkns, abj t`at t`n rnsnari` ms rnkmafkn, m.n. Mt ymnkjs icbsmstnbt rnsukts nvnry tmon. Tart ce t`n rnsnari`

ont`cjckchy ms icbinrbnj wmt` t`n `cw t`n rnsnari` ms icbjuitnj. Z`ms ms iakknj t`n stujy jnsmhb abj typmiakky mbvckvns

rnsnari` icbjuitnj usmbh qunstmcbbamrns, mbtnrvmnws, cfsnrvatmcb abj/cr nxpnrmonbts.

Z`n tnro rnsnari` ont`cjckchy, aksc rnenrrnj tc as rnsnari` ont`cjs, usuakky nbicopassns t`n prcinjurns eckkcwnj

tc abakyzn abj mbtnrprnt t`n jata hat`nrnj. Z`nsn cetnb usn a rabhn ce scp`mstmiatnj statmstmiak abakysns ce t`n jata tc

mjnbtmey icrrnkatmcbs cr statmstmiak smhbmemiabin mb t`n rnsukts. Cfgnitmvn, rnprnsnbtatmvn rnsnari` iab fn jmeemiukt tc icbjuit

fniausn tnsts iab bcroakky cbky fn icbjuitnj cb a soakk saopkn (n.h. ]cu iabbct tnst a jruh cb nvnry pnrscb mb t`n wcrkj

sc a saopkn bnnjs tc fn usnj mb rnsnari`). Z`ms onabs t`at rnsnari`nrs bnnj tc `avn a vnry jntamknj ubjnrstabjmbh ce t`n

typns abj kmomtatmcbs ce rnsnari` ont`cjckchmns w`mi` t`ny arn usmbh.

Z`n prcinjurak ont`cjckchy ms apprcprmatn ecr mbtnhratmbh t`n varmcus rnqumrnonbts ecr jcmbh rnsnari` abj mt fumkjs

frmjhns aircss jmeenrnbt quakmtatmvn ont`cjs, ont`cjckchy, abj icbtnopcrary scimnty abakysms, gust as fntwnnb scimak

abj nbvmrcbonbtak rnsnari`. Mts oamb i`araitnrmstmis arn wcrlnj cut as prcinjurakmty, snqunbtmakmty, ouktmjmonbsmcbakmty,

rneknxmvmty, abj trabsjmsimpkmbarmty.

]cur rnsnari` wmkk jmitatn t`n lmbjs ce rnsnari` ont`cjckchmns ycu usn tc ubjnrpmb ycur wcrl abj ont`cjs ycu usn

mb crjnr tc ickknit jata. Me ycu wms` tc ickknit quabtmtatmvn jata ycu arn prcfafky onasurmbh varmafkns abj vnrmeymbhnxmstmbh t`ncrmns cr ypct`nsns cr qunstmcbmbh t`no. Jata ms cetnb usnj tc hnbnratn bnw ypct`nsns fasnj cb t`n rnsukts ce

jata ickknitnj afcut jmeenrnbt varmafkns. Cbns ickknahuns arn cetnb oui` `appmnr afcut t`n afmkmty tc vnrmey quabtmtatmvn

jata as oaby pncpkn ennk saen cbky wmt` buofnrs abj statmstmis.

@cwnvnr, cetnb ickknitmcbs ce statmstmis abj buofnr irubi`mbh arn bct t`n abswnr tc ubjnrstabjmbh onabmbhs, fnkmnes

abj nxpnrmnbin, w`mi` arn fnttnr ubjnrstccj t`rcuh` quakmtatmvn jata. Abj quabtmtatmvn jata, mt oust fn rnonofnrnj, arn

aksc ickknitnj mb aiicrjabin wmt` inrtamb rnsnari` vn`mikns abj ubjnrkymbh rnsnari` qunstmcbs. Nvnb t`n prcjuitmcb ce

buofnrs ms humjnj fy t`n lmbjs ce qunstmcbs aslnj ce t`n sufgnits, sc ms nssnbtmakky sufgnitmvn, akt`cuh` mt appnars knss sc

t`ab quakmtatmvn rnsnari` jata.

AYYMHBONBZ YCK^ZMCBY H^MJN (641:-641>)

O.I.C.-9

Vnsnari` Ont`cjckchy abj Ytatmstmiak AbakysmsJmsikamonr/Ypnimak Bctn7Z`nsn arn gust t`n saopkn ce t`n Abswnrs/Yckutmcbs tc scon ce t`n Qunstmcbs hmvnb mb t`nAssmhbonbts. Z`nsn Yaopkn Abswnrs/Yckutmcbs arn prnparnj fy Trmvatn Znai`nr/Zutcrs/Au tcrs ecr t`n `nkp abj Humjabin

ce t`n stujnbt tc hnt ab mjna ce cw n/s`n iab abswnr t`n Qunstmcbs ce t`n Assmhbonbts. Xn jc bct ikamo 144% Aiiuraiy

ce t`nsn saopkn Abswnrs as t`nsn arn fasnj cb t`n lbcwknjhn abj iafafmkmty ce Trmvatn Znai`nr/Zutcr. Yaopkn abswnrs

oay fn snnb as t`n Humjn/@nkp Fccl ecr t`n rnenrnbin tc prnparn t`n abswnrs ce t`n Qunstmcb hmvnb mb t`n assmhbonbt. As

t`nsn sckutmcbs abj abswnrs arn prnparnj fy t`n prmvatn tnai`nr/tutcr sc t`n i`abins ce nrrcr cr omstaln iabbct fn jnbmnj.

Aby Comssmcb cr Nrrcr ms `mh`ky rnhrnttnj t`cuh` nvnry iarn `as fnnb talnb w`mkn prnparmbh t`nsn Yaopkn Abswnrs/Yckutmcbs. Tknasn icbsukt ycur cwb Znai`nr/Zutcr fnecrn ycu prnparn a Tartmiukar Abswnr & ecr uptcjatn abj nxait

mbecroatmcb, jata abj sckutmcb. Ytujnbt s`cukj oust rnaj abj rnenr t`n ceemimak stujy oatnrmak prcvmjnj fy t`n ubmvnrsmty.

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Q. 6. (a)X`at jc ycu onab fy Vnsnari` Jnsmhb3 Jmsiuss t`n rckn ce rnsnari` jnsmhb mb fusmbnss rnsnari`.

Abs.Z`n rnsnari` jnsmhb rnenrs tc t`n cvnrakk stratnhy t`at ycu i`ccsn tc mbtnhratn t`n jmeenrnbt icopcbnbts ce t`n

stujy mb a ic`nrnbt abj kchmiak way, t`nrnfy, nbsurmbh ycu wmkk neenitmvnky ajjrnss t`n rnsnari` prcfkno< mt icbstmtutns t`n

fkunprmbt ecr t`n ickknitmcb, onasurnonbt, abj abakysms ce jata. Bctn t`at ycur rnsnari` prcfkno jntnrombns t`n typn ce

jnsmhb ycu iab usn, bct t`n ct`nr way arcubj! Z`n eubitmcb ce a rnsnari` jnsmhb ms tc nbsurn t`at t`n nvmjnbin cftambnj

nbafkns ycu tc neenitmvnky ajjrnss t`n rnsnari` prcfkno kchmiakky abj as ubaofmhucusky as pcssmfkn. Mb scimak simnbins

rnsnari`, cftambmbh mbecroatmcb rnknvabt tc t`n rnsnari` prcfkno hnbnrakky nbtamks spnimeymbh t`n typn ce nvmjnbin bnnjnj

tc tnst a t`ncry, tc nvakuatn a prchrao, cr tc aiiuratnky jnsirmfn abj assnss onabmbh rnkatnj tc ab cfsnrvafkn p`nbconbcb.

Xmt` t`ms mb ombj, a icoocb omstaln oajn fy rnsnari`nrs ms t`at t`ny fnhmb t`nmr mbvnstmhatmcbs ear tcc narky, fnecrnt`ny `avn t`cuh`t irmtmiakky afcut afcut w`at mbecroatmcb ms rnqumrnj tc ajjrnss t`n stujys rnsnari` qunstmcbs. Xmt`cut

attnbjmbh tc t`nsn jnsmhb mssuns fnecrn`abj, t`n cvnrakk rnsnari` prcfkno wmkk bct fn ajnquatnky ajjrnssnj abj aby

icbikusmcbs jrawb wmkk rmsl fnmbh wnal abj ubicbvmbimbh. As a icbsnqunbin, t`n cvnrakk vakmjmty ce t`n stujy wmkk fn

ubjnrombnj.

A rnsnari` jnsmhb ms a systnoatmi pkab tc stujy a simnbtmemi prcfkno. Z`n jnsmhb ce a stujy jnembns t`n stujy typn

(jnsirmptmvn, icrrnkatmcbak, snom-nxpnrmonbtak, nxpnrmonbtak, rnvmnw, onta-abakytmi) abj suf-typn (n.h., jnsirmptmvn-kcbhm-

tujmbak iasn stujy), rnsnari` qunstmcb, `ypct`nsns, mbjnpnbjnbt abj jnpnbjnbt varmafkns, nxpnrmonbtak jnsmhb, abj, me

appkmiafkn, jata ickknitmcb ont`cjs abj a statmstmiak abakysms pkab. Vnsnari` jnsmhb ms t`n eraonwcrl t`at `as fnnb irnatnj

tc snnl abswnrs tc rnsnari` qunstmcbs.

Z`n rckn ce rnsnari` mb fusmbnss ms tc prcvmjn mbecroatmcb t`at iab `nkp ycur icopaby rub neemimnbtky abj prcemtafky.

A wnkk rnsnari`nj fusmbnss `as ab ajvabtahn cvnr mts icopntmtcrs fniausn mts prmbimpaks pkab fusmbnss cpnratmcbs mbrnenrnbin tc aituak, vnrmemnj jata rat`nr t`ab spniukatmvn hunssns. Z`ms ombmomzns icstky omstalns abj neenitmvnky eciusns

oarlntmbh neecrts.

Iustconr-fasnj Oarlntmbh Vnsnari`7Iustconr-fasnj oarlntmbh rnsnari` prcvmjns ycur icopaby wmt` nssnbtmak

mbecroatmcb afcut w`at ycur ikmnbtnkn wabts, abj w`nt`nr ycur icopaby ms neenitmvnky prcvmjmbh mt. Oarlntmbh rnsnari`

iab taln t`n ecro ce ecroak survnys sui` as cbkmbn pckks cr mb-pnrscb qunstmcbbamrns wmt` spnimemi cfgnitmvns nvakuatmbh

w`nt`nr cr bct t`nrn ms a oarlnt ecr ycur bnw mjna.

Trcjuit Vnsnari`7Trcjuit rnsnari` prcvmjns ycu wmt` t`n mbecroatmcb ycu bnnj tc irnatn jurafkn, `mh`-quakmty

ceenrmbhs. Me ycu cwb a tcy oabueaiturmbh icopaby, tnstmbh bnw prcjuits wcukj mbvckvn sufgnitmbh t`no tc t`n typn ce

`ars` trnatonbt t`ny omh`t nbjurn at t`n `abjs ce i`mkjrnb tc nbsurn t`ny arn sturjy abj saen, as wnkk as prcvmjmbh

prctctypns tc i`mkjrnb tc oaln surn t`ny nbgcy usmbh t`no. Me ycu cwb a eccj fusmbnss, prcjuit rnsnari` omh`t mbikujn

tnstmbh prcjuit s`nke kmen fy tastmbh eccjs aetnr jmeenrnbt pnrmcjs ce tmon.

Cpnratmcbs Vnsnari 7Zc neenitmvnky oabueaiturn abj oarlnt ycur prcjuit, ycur icopaby oust rnsnari` mbecroa-

tmcb afcut t`n fnst way tc prcjuin abj jmstrmfutn mt. Z`ms rnsnari` mbvckvns mbvnstmhatmbh prcjuitmcb prcinssns abj nqump-

onbt, as wnkk as scurins ecr suppkmns abj oatnrmaks. Fy jcmbh ycur `conwcrl abj i`ccsmbh t`n ocst apprcprmatn nqump-

onbt, ycur icopaby wmkk savn t`n tmon abj strnss ce usmbh ikuosy, mbneemimnbt systnos.

Icopntmtcr-fasnj Oarlntmbh Vnsnari`7Icopntmtcr-fasnj oarlntmbh rnsnari` prcvmjns mbecroatmcb bninssary tc

suiinsseukky mbtrcjuin abj frabj ycur prcjuit. Icopntmtcr rnsnari` mbikujns stujymbh icoparafkn prcjuits tc `mh`kmh`t

ways t`at ycur cwb ceenrmbhs arn jmeenrnbt. Mt aksc mbvckvns rnsnari`mbh t`n prmins cb mtnos mb ycur mbjustry tc ubjnrstabj

w`at iustconrs wmkk typmiakky pay, abj aksc tc jnvnkcp a prmimbh stratnhy t`at frabjs ycur prcjuit rnkatmvn tc t`n ct`nr

avamkafkn aktnrbatmvns. Cfsnrvmbh oarlntmbh stratnhmns t`at ycur icopntmtcrs usn nbafkns ycu tc ubjnrstabj ycur tarhnt

oarlnt, abj stratnhmzn afcut ways tc rnai` t`no.

(f)X`at arn t`n oamb mssuns a rnsnari`nr eains mb ecroukatmbh a rnsnari` prcfkno3 Ecroukatn emvn rnsnari`

prcfknos mb nai` eubitmcbak arnas ce fusmbnss.Abs.A rnsnari` prcfkno ms a statnonbt afcut ab arna ce icbinrb, a icbjmtmcb tc fn moprcvnj upcb, a jmeemiukty tc fn

nkmombatnj, cr a trcufkmbh qunstmcb t`at nxmsts mb si`ckarky kmtnraturn, mb t`ncry, cr mb praitmin t`at pcmbts tc t`n bnnj ecr

onabmbheuk ubjnrstabjmbh abj jnkmfnratn mbvnstmhatmcb. Mb scon scimak simnbin jmsimpkmbns t`n rnsnari` prcfkno ms typm-

iakky pcsnj mb t`n ecro ce cbn cr ocrn qunstmcbs. A rnsnari` prcfkno jcns bct statn `cw tc jc scont`mbh, ceenr a vahun

cr frcaj prcpcsmtmcb, cr prnsnbt a vakun qunstmcb. Tnr`aps t`n ocst mopcrtabt part ce rnsnari` ms ecroukatmbh a rnsnari`

prcfkno. Ecroukatmbh a rnsnari` prcfkno s`cws a rnsnari`nr w`nrn prnvmcus rnsnari`nrs `avn fnnb jnemimnbt abj mjnbtm-

emns avnbuns ce stujy t`at `avn bct ynt fnnb pursunj. Vnsnari`nrs oust fn iarneuk tc ecroukatn t`nmr rnsnari` prcfknos

prcpnrky mb crjnr tc oaln surn t`at t`nmr rnsnari` mbtnbt ms bct aofmhucus, abj tc oaln surn t`at t`n mbecroatmcb cftambnj

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t`rcuh` t`n rnsnari` ms ce smhbmemiabin.

Vnsnari` Trcfkno7 Emvn Xays tc Ecroukatn t`n Vnsnari` Trcfkno

1. Ypnimey t`n Vnsnari` Cfgnitmvns7A iknar statnonbt ce cfgnitmvns wmkk `nkp ycu jnvnkcp neenitmvn rnsnari`. Mt wmkk

`nkp t`n jnimsmcb oalnrs nvakuatn ycur prcgnit. Mts irmtmiak t`at ycu avn oabahnafkn cfgnitmvns. (Zwc cr t`rnn iknar hcaks

wmkk `nkp tc lnnp ycur rnsnari` prcgnit eciusnj abj rnknvabt.)

6. Jnembn t`n Uarmafkn Vnkatmcbs`mps7Oarlntmbh pkabs cetnb ecius cb irnatmbh a snqunbin ce fn`avmcurs t`at ciiur

cvnr tmon, as mb t`n ajcptmcb ce a bnw pailahn jnsmhb, cr t`n mbtrcjuitmcb ce a bnw prcjuit. Yui` prchraos irnatn a

icoomtonbt tc eckkcw scon fn`avmcrak pattnrb mb t`n euturn.

9. Z`n Icbsnqunbins ce Aktnrbatmvn Icursns ce Aitmcb7Z`nrn arn akways icbsnqunbins tc aby icursn ce aitmcb.

Abtmimpatmbh abj icooubmiatmbh t`n pcssmfkn cuticons ce varmcus icursns ce aitmcb ms a prmoary rnspcbsmfmkmty mb t`n

rnsnari` prcinss.

:. Vnvmnw t`n Nbvmrcbonbt cr Icbtnxt ce t`n Vnsnari` Trcfkno7As a oarlntmbh rnsnari`nr, ycu oust wcrl

ikcsnky wmt` ycur tnao. Z`ms wmkk `nkp ycu jntnrombn w`nt`nr t`n embjmbhs ce ycur prcgnit wmkk prcjuin nbcuh` mbecroa-

tmcb tc fn wcrt` t`n icst. Mb crjnr tc jc t`ms, ycu `avn tc mjnbtmey t`n nbvmrcbonbtak varmafkns t`at wmkk aeenit t`n rnsnari`

prcgnit.

>. Nxpkcrn t`n Baturn ce t`n Trcfkno7Vnsnari` prcfknos rabhn erco smopkn tc icopknx, jnpnbjmbh cb t`n buofnr

ce varmafkns abj t`n baturn ce t`nmr rnkatmcbs`mp. Me ycu ubjnrstabj t`n baturn ce t`n prcfkno as a rnsnari`nr, ycu wmkk fn

afkn tc fnttnr jnvnkcp a sckutmcb ecr t`n prcfkno. Zc `nkp ycu ubjnrstabj akk jmonbsmcbs, ycu omh`t wabt tc icbsmjnr

ecius hrcups ce icbsuonrs, sakns pncpkn, oabahnrs, cr prcenssmcbaks tc prcvmjn w`at ms scontmons oui` bnnjnj mbsmh`t.

Q. 9. (a)Jmsiuss t`n irmtnrma ecr wcrlafkn `ypct`nsms wmt` sumtafkn nxaopkns.Abs.A wcrlmbh `ypct`nsms ms a `ypct`nsms t`at ms prcvmsmcbakky aiinptnj as a fasms ecr eurt`nr rnsnari` mb t`n `cpn

t`at a tnbafkn t`ncry wmkk fn prcjuinj, nvnb me t`n `ypct`nsms uktmoatnky eamks. Kmln akk `ypct`nsns, a wcrlmbh `ypct`nsms

ms icbstruitnj as a statnonbt ce nxpnitatmcbs, w`mi` iab fn kmblnj tc t`n nxpkcratcry rnsnari` purpcsn mb nopmrmiak

mbvnstmhatmcb abj ms cetnb usnj as a icbinptuak eraonwcrl mb quakmtatmvn rnsnari`. A `ypct`nsms ms ab nxpkabatmcb ecr a snt

ce cfsnrvatmcbs. @nrn arn nxaopkns ce a simnbtmemi `ypct`nsms. Akt`cuh` ycu icukj statn a simnbtmemi `ypct`nsms mb varmcus

ways, ocst ypct`nsms arn nmt`nr Me, t`nb statnonbts cr nksn ecros ce t`n bukk ypct`nsms. Z`n bukk ypct`nsms scontmons

ms iakknj t`n bc jmeenrnbin `ypct`nsms. Z`n bukk `ypct`nsms ms hccj ecr nxpnrmonbtatmcb fniausn mts smopkn tc jmsprcvn.

Me ycu jmsprcvn a bukk `ypct`nsms, t`at ms nvmjnbin ecr a rnkatmcbs`mp fntwnnb t`n varmafkns ycu arn nxaombmbh.

Z`n Bukk abj Aktnrbatmvn @ypct`nsns

Z`n ikamo fnmbh mbvnstmhatnj ms t`at t`n avnrahn fcjy tnopnraturn ce 18 ynar ckjs ms hrnatnr t`ab =0.5 jnhrnns Z`ms

icrrnspcbjs tc t`n statnonbt x 3 =0.5. Z`n bnhatmcb ce t`ms ms t`at t`n pcpukatmcb avnrahn ms bct hrnatnr t`ab =0.5 jnhrnns.

Mb ct`nr wcrjs t`n avnrahn tnopnraturn ms knss t`ab cr nquak tc =0.5 jnhrnns. Mb syofcks t`ms ms x ; =0.5.

Cbn ce t`nsn statnonbts oust fnicon t`n bukk ypct`nsms, abj t`n ct`nr s`cukj fn t`n aktnrbatmvn ypct`nsms. Z`n bukk

`ypct`nsms icbtambs nquakmty. Yc ecr t`n afcvn, t`n bukk `ypct`nsms @4 7 x ? =0.5. Mt ms icoocb praitmin tc cbky statn t`n

bukk `ypct`nsms mb tnros ce ab nquaks smhb, abj bct a hrnatnr t`ab cr nquak tc cr knss t`ab cr nquak tc.

Z`n statnonbt t`at jcns bct icbtamb nquakmty ms t`n aktnrbatmvn `ypct`nsms, cr @1 7 x 2=0.5.

Z`n statnonbt ce cur prcfkno wmkk jntnrombn w`mi` lmbj ce tnst tc usn. Me t`n aktnrbatmvn `ypct`nsms icbtambs a bct

nquaks tc smhb, t`nb wn `avn a twc tamknj tnst. Mb t`n ct`nr twc iasns, w`nb t`n aktnrbatmvn `ypct`nsms icbtambs a strmit

mbnquakmty, wn usn a cbn tamknj tnst. Z`ms ms cur smtuatmcb, sc wn usn a cbn tamknj tnst.

I`cmin ce a Ymhbmemiabin Knvnk7@nrn wn i`ccsn t`n vakun ce akp`a, cur smhbmemiabin knvnk. Mt ms typmiak tc knt akp`a fn

4.4> cr 4.41. Ecr t`ms nxaopkn wn wmkk usn a >% knvnk abj akp`a wmkk fn nquak tc 4.4>.

I`cmin ce Znst Ytatmstmi abj Jmstrmfutmcb7Bcw wn bnnj tc jntnrombn w`mi` jmstrmfutmcb tc usn. Z`n saopkn ms erco

a pcpukatmcb t`at ms bcroakky jmstrmfutnj as t`n fnkk iurvn, sc wn iab usn t`n stabjarj bcroak jmstrmfutmcb. A tafkn ce z-sicrns wmkk fn bninssary.

(f)Nxpkamb t`n prcinjurn ecr tnstmbh ce `ypct`nsms.

Abs.Trcinjurn ecr Znstmbh @ypct`nsms7Zc tnst a `ypct`nsms onabs tc tnkk (cb t`n fasms ce t`n jata rnsnari`nr `as

ickknitnj) w`nt`nr cr bct t`n `ypct`nsms snnos tc fn vakmj. Mb `ypct`nsms tnstmbh t`n oamb qunstmcb ms7 w`nt`nr t`n bukk

`ypct`nsms cr bct tc aiinpt t`n bukk ypct`nsms3 Trcinjurn ecr ypct`nsms tnstmbh rnenrs tc akk t`csn stnps t`at wn ubjnrtaln

ecr oalmbh a i`cmin fntwnnb t`n twc aitmcbs m.n., rngnitmcb abj aiinptabin ce a bukk `ypct`nsms. Z`n varmcus stnps mb-

vckvnj mb `ypct`nsms tnstmbh arn statnj fnkcw7

(1) Oalmbh a Ecroak Ytatnonbt7Z`n stnp icbsmsts mb oalmbh a ecroak statnonbt ce t`n bukk `ypct`nsms (@c) abj

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aksc ce t`n aktnrbatmvn `ypct`nsms (@a). Z`ms onabs t`at `ypct`nsms s`cukj iknarky statn, icbsmjnrmbh t`n baturn ce t`n

rnsnari` prcfkno. Ecr mbstabin, Or. P ce t`n Imvmk Nbhmbnnrmbh Jnpartonbt wabts tc tnst t`n kcaj fnarmbh iapaimty ce ab

ckj frmjhn w`mi` oust fn ocrn t`ab 14 tcbs, mb t`at iasn `n iab statn `ms `ypct`nsms as ubjnr7

Bukk `ypct`nsms @C7 ?14 tcbs

Aktnrbatmvn ypct`nsms @a7 214 tcbs

Zaln abct`nr nxaopkn. Z`n avnrahn sicrn mb ab aptmtujn tnst ajombmstnrnj at t`n batmcbak knvnk ms 04. Zc nvakuatn a

statns njuiatmcb systno, t`n avnrahn sicrn ce 144 ce t`n statns stujnbts snknitnj cb t`n rabjco fasms was 8>. Z`n statn

wabts tc lbcw me t`nrn ms a smhbmemiabin jmeenrnbin fntwnnb t`n kciak sicrns abj t`n batmcbak sicrns. Mb sui` a smtuatmcb t`n

`ypct`nsms oay fn statn as ubjnr7

Bukk `ypct`nsms @C7 ?04

Aktnrbatmvn `ypct`nsms @a7 3 04

Z`n ecroukatmcb ce ypct`nsms ms ab mopcrtabt stnp w`mi` oust fn aiicopkms`nj wmt` jun iarn mb aiicrjabin wmt` t`n

cfgnit abj baturn ce t`n prcfkno ubjnr icbsmjnratmcb. Mt aksc mbjmiatns w`nt`nr wn s`cukj usn a tamknj tnst cr a twc tamknj

tnst. Me `a ms ce t`n typn hrnatnr t`ab, wn usn akcbn tamknj tnst, fut w`nb @a ms ce t`n typn w`nt`nr hrnatnr cr soakknr t`nb

wn usn a twc-tamknj tnst.

6) Ynknitmbh a Ymhbmemiabt Knvnk7Z`n `ypct`nsms ms tnstnj cb a prn-jntnrombnj knvnk ce smhbmemiabin abj sui` t`n

saon s`cukj avn spnimemnj. Hnbnrakky, mb praitmin, nmt`nr >% knvnk cr 1% knvnk ms ajcptnj ecr t`n purpcsn. Z`n eaitcrs t`at

aeenit t`n knvnk ce smhbmemiabin arn7

Z`n oahbmtujn ce t`n jmeenrnbin fntwnnb saopkn . (a)Jmsiuss t`n usneukbnss ce I`m-squarn tnst mb fusmbnss rnsnari`. X`at arn t`n nssnbtmak icbjmtmcbs ecr

appkymbh I`m-squarn tnst3

Abs.I`m-squarn ms a statmstmiak tnst icoocbky usnj tc icoparn cfsnrvnj jata wmt` jata wn wcukj nxpnit tc cftamb

aiicrjmbh tc a spnimemi `ypct`nsms. Ecr nxaopkn, me, aiicrjmbh tc Onbjnks kaws, ycu nxpnitnj 14 ce 64 ceesprmbh erco a

ircss tc fn oakn abj t`n aituak cfsnrvnj buofnr was 0 oakns, t`nb ycu omh`t wabt tc lbcw afcut t`n hccjbnss tc emt

fntwnnb t`n cfsnrvnj abj nxpnitnj. Xnrn t`n jnvmatmcbs (jmeenrnbins fntwnnb cfsnrvnj abj nxpnitnj) t`n rnsukt ce

i`abin, cr wnrn t`ny jun tc ct`nr eaitcrs. @cw oui` jnvmatmcb iab ciiur fnecrn ycu, t`n mbvnstmhatcr, oust icbikujn t`at

scont`mbh ct`nr t`ab i`abin ms at wcrl, iausmbh t`n cfsnrvnj tc jmeenr erco t`n nxpnitnj. Z`n i`m-squarn tnst ms akways

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tnstmbh w`at simnbtmsts iakk t`n bukk `ypct`nsms, w`mi` statns t`at t`nrn ms bc smhbmemiabt jmeenrnbin fntwnnb t`n nxpnitnj

abj cfsnrvnj rnsukt. Z`n i`m-squarn (i6) tnst onasurns t`n akmhbonbt fntwnnb twc snts ce ernqunbiy onasurns. Z`nsn

oust fn iatnhcrmiak icubts abj bct pnrinbtahns cr ratmcs onasurns (ecr t`nsn, usn abct`nr icrrnkatmcb tnst). Bctn t`at t`n

ernqunbiy buofnrs s`cukj fn smhbmemiabt abj fn at knast afcvn emvn (akt`cuh` ab ciiasmcbak kcwnr emhurn oay fn pcssmfkn,

as kcbh as t`ny arn bct a part ce a pattnrb ce kcw emhurns).

Hccjbnss ce emt7A icoocb usn ms tc assnss w`nt`nr a onasurnj/cfsnrvnj snt ce onasurns eckkcws ab nxpnitnj

pattnrb. Z`n nxpnitnj ernqunbiy oay fn jntnrombnj erco prmcr lbcwknjhn (sui` as a prnvmcus ynars nxao rnsukts) cr fy

iakiukatmcb ce ab avnrahn erco t`n hmvnb jata.

Z`n bukk `ypct`nsms, @4ms t`at t`n twc snts ce onasurns arn bct smhbmemiabtky jmeenrnbt.

Mbjnpnbjnbin7 Z`n i`m-squarn tnst iab fn usnj mb t`n rnvnrsn oabbnr tc hccjbnss ce emt. Me t`n twc snts ce onasurns

arn icoparnj, t`nb gust as ycu iab s`cw t`ny akmhb, ycu iab aksc jntnrombn me t`ny jc bct akmhb.

Z`n bukk `ypct`nsms `nrn ms t`at t`n twc snts ce onasurns arn smomkar.

Z`n oamb jmeenrnbin mb hccjbnss-ce-emt vs. mbjnpnbjnbin assnssonbts ms mb t`n usn ce t`n I`m Yquarn tafkn. Ecr

hccjbnss ce emt, attnbtmcb ms cb 4.4>, 4.41 cr 4.441 emhurns. Ecr mbjnpnbjnbin, mt ms cb 4.=> cr 4.== emhurns (t`ms ms w`y t`n

tafkn `as twc nbjs tc mt).

Nxaopkn

Hccjbnss ce emt7Nbhkms` tnst hrajn jmstrmfutmcbs `avn i`abhnj erco kast ynar, wmt` hrajn Fs sconw`at kcwnr.

Zc icbjuit t`n i`m-squarn tnst, t`n rnsnari`nr nbtnrs cfsnrvnj ernqunbimns icrrnspcbjmbh tc icofmbatmcbs ce knvnks ce

rnknvabt eaitcrs (`nrn, iakknj icbjmtmcb abj hrcup, fut t`nsn arn kafnks ce icbvnbmnbin). Yuos ce nknonbts wmt`mb

rcws abj wmt`mb ickuobs arn t`nb icoputnj (iakk t`nsn oarhmbak Bs). Z`n i`m-squarn tnst ce mbjnpnbjnbin ms usnj tc tnstt`n bukk `ypct`nsms t`at t`n ernqunbiy wmt`mb inkks ms w`at wcukj fn nxpnitnj, hmvnb t`nsn oarhmbak Bs. Z`n i`m-squarn

tnst ce hccjbnss ce emt ms usnj tc tnst t`n `ypct`nsms t`at t`n tctak saopkn B ms jmstrmfutnj nvnbky aocbh akk knvnks ce t`n

rnknvabt eaitcr.

Z`n nxpnitnj vakun wmt`mb nai` inkk, me t`n bukk icbjmtmcb ms trun (m.n., me t`n eaitcrs `avn bc smhbmemiabt mbekunbin cb

cfsnrvnj ernqunbimns mb t`n pcpukatmcb), ms smopky t`n prcjuit ce t`n rcw tctak abj ickuob tctak jmvmjnj fy t`n cvnrakk

saopkn B ecr t`n tnst ce mbjnpnbjnbin abj B jmvmjnj fy t`n buofnr ce knvnks ce t`n smbhkn eaitcr ecr t`n tnst ce hccjbnss

ce emt. Me Cmg ms t`n cfsnrvnj ernqunbiy abj Nmg t`n nxpnitnj ernqunbiy ecr t`n inkk icrrnspcbjmbh tc t`n mt` icbjmtmcb abj

t`n gt` hrcup, t`nb i`m-squarn ms7

P6 ?

6

9 9

9

(C N )

Nm g

Me t`nrn ms cbky cbn eaitcr ce mbtnrnst wmt` (l 2 1) knvnks, t`n saon ecrouka wmkk wcrl, wmt` m cr g fnmbh snt tc 1. Z`n tnst

prnsnbtnj `nrn iab fn usnj tc tnst cbky 1- cr 6-jmonbsmcbak arrays.

(f)X`y jc wn stujy prcfafmkmty3 Nxpkamb t`n prcinjurn mbvckvnj mb emttmbh fmbcomak abj icbtmbucus prcf-

afmkmty jmstrmfutmcb.

Abs.Trcfafmkmty ms usnj tc quabtmey ab attmtujn ce ombj tcwarjs scon prcpcsmtmcb ce w`csn trut` wn arn bct inrtamb.

Z`n prcpcsmtmcb ce mbtnrnst ms usuakky ce t`n ecro Xmkk a spnimemi nvnbt ciiur3 Z`n attmtujn ce ombj ms ce t`n ecro @cw

inrtamb arn wn t`at t`n nvnbt wmkk ciiur3 Z`n inrtambty wn ajcpt iab fn jnsirmfnj mb tnros ce a buonrmiak onasurn abj

t`ms buofnr, fntwnnb 4 abj 1 (w`nrn 4 mbjmiatns mopcssmfmkmty abj 1 mbjmiatns inrtambty), wn iakk prcfafmkmty. Z`us t`n

`mh`nr t`n prcfafmkmty ce ab nvnbt, t`n ocrn inrtamb wn arn t`at t`n nvnbt wmkk ciiur. A smopkn nxaopkn wcukj fn t`n tcss

ce a eamr icmb. Ymbin t`n 6 cuticons arn jnnonj nqum-prcfafkn, t`n prcfafmkmty ce `najs nquaks t`n prcfafmkmty ce tamks

abj nai` prcfafmkmty ms 1/6 cr nqumvaknbtky a >4% i`abin ce nmt`nr `najs cr tamks. Trcfafmkmty iab fn rnprnsnbtnj

buonrmiakky wmt` a buofnr fntwnnb znrc abj cbn, wmt` znrc rnprnsnbtmbh t`n mopcssmfmkmty ce scont`mbh spnimemi `appnb-

mbh abj cbn rnprnsnbtmbh t`n inrtambty ce t`at t`mbh appnbmbh. Z`ms buofnr ms cetnb trabsenrrnj tc a pnrinbtahn mb crjnr tc

prnjmit scont`mbh usneuk, sui` as a wnat`nr pnrscb prnjmitmbh t`n kmlnkm`ccj ce ramb cb t`n eckkcwmbh jay. Yui` ab

mbjmvmjuak usns prcfafmkmty fy talmbh avamkafkn jata cb wnat`nr abj oalmbh t`n ocst aiiuratn prnjmitmcb pcssmfkn. Trcf-

afmkmty t`ncry jmeenrs erco statmstmis fniausn statmstmis rnqumrns t`n nxaombatmcb ce w`at `as akrnajy ciiurrnj mb crjnr tc

jntnrombn `cw sui` a rnsukt ciiurrnj. Cbn ernqunbt usn ce prcfafmkmty ms t`n jntnrombatmcb ce nvnbts t`at arn neenitmvnky

mopcssmfkn tc qumilky prnjmit w`nb a rabjco jntnrombatmcb bnnjs tc fn oajn. Z`ms ms icoocbky snnb mb spcrtmbh nvnbts

mb w`mi` a icmb ekmp iab mbekunbin aspnits ce t`n haon. Mb trut`, a icmb ekmp iab fn mbekunbinj fy eaitcrs sui` as icmb spnnj,

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fut t`n rnkatmvn mopcssmfmkmty ce usmbh t`ms mbecroatmcb tc prnjmit w`mi` smjn t`n icmb kabjs cb oalns mt a usneuk tcck ecr

arfmtrary jntnrombatmcbs.

X`nb icbercbtnj wmt` jata t`at bnnjs tc fn i`araitnrmznj fy a jmstrmfutmcb, mt ms fnst tc start wmt` t`n raw jata abj

abswnr ecur fasmi qunstmcbs afcut t`n jata t`at iab `nkp mb t`n i`araitnrmzatmcb. Z`n emrst rnkatns tc w`nt`nr t`n jata iab

taln cb cbky jmsirntn vakuns cr w`nt`nr t`n jata ms icbtmbucus< w`nt`nr a bnw p`aroainutmiak jruh hnts EJA apprcvak cr

bct ms a jmsirntn vakun fut t`n rnvnbuns erco t`n jruh rnprnsnbt a icbtmbucus varmafkn. Z`n snicbj kccls at t`n syoontry

ce t`n jata abj me t`nrn ms asyoontry, w`mi` jmrnitmcb mt kmns mb< mb ct`nr wcrjs, arn pcsmtmvn abj bnhatmvn cutkmnrs nquakky

kmlnky cr ms cbn ocrn kmlnky t`ab t`n ct`nr. Z`n t`mrj qunstmcb ms w`nt`nr t`nrn arn uppnr cr kcwnr kmomts cb t`n jata