1 Conceptos Básicos de La Estadística

 

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JKWCÀO KWOKX]L WBOHØO WKR

[OBM@MKX ]KHOLFØJBH@X MK X@O]@OMKW G[H@W@C@OJ@ 7401

 

[OBM@MKX ]KHOLFLJBH@X ]KHOLFLJBH@X MK X@ O]@OMKW KX]@MÃX]BH@ KX]@MÃX]B H@ MKXHWBT]B^@ MKXHWBT]B^@ R TWBOHBTBLX TWBOHBTBLX MK TWLG@G BFBM@M

Wkhtlr

Lc`r Fkojkrek Târkz

Hllrmbo`mlr Mkp`rt`ckotl mk Hbkohb`s Gàsbh`s

Knrâo M`vbm Clotks ^kr`

Kst`mãstbh` mkshrbptbv` y prbohbpbls mk Trlg`gbfbm`m 7401. Trbckr` kmbhbøo

Jkrcào Krokstl Wbohøo Wky

 

 

0. @WWKJFL R TWKXKO]@HBØO MK M@]LX 

0.0 BO]WLM[HHBØO

¼Tlr quâ ks okhks`rb` f` kst`mãstbh kst`mãstbh `< ]lm`s f`s pkrslo`s, ko cuhals clckotls mk sus vbm`s okhksbt`o tlc`r

mkhbsbloks. Kst`s mkhbsbloks slo càs nàhbfks mk tlc`r y fls rksuft`mls mk kff`s càs `mkhu`mlss sb9 `mkhu`ml

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  Xk hlolhk hlcl v` ` kvlfuhblo`r f` sbtu`hbøo l aakhal khal slgrk f` quk sk v` ` tlc`r f` mkhbsbøo

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  Xk hlolhk kf hlcplrt`cb hlcplrt`cbkotl kotl jkokr`f mk f` sbtu`hb sbtu`hbøo øo l akhal mk botkrâs p`r` tlc`r f` mkhbsbøo.

 @ kstls hlombhblo`cbkotls sk fks ff`c` ‖bonlrc`hbøo–.

Hlcl f` bonlrc`hbøo ol kstà sbkcprk mbsplobgfk l o l sk kohukotr` mbspukst` mk f` nlrc` `mkhu`m` p`r` su utbfbz`hbøo ko kf prlhksl mkhbslrbl, a`y, kotlohks, quk hlostrubrf`. T`r` lgtkokr bonlrc`hbøo sk p`rtk mk m`tls, mbsplobgfks u lgtkobmls p`r` kf prlpøsbtl ko hukstbøo, prlhks`oml mk mbvkrs`s nlrc`s kstls m`tls, a`st` lgtkokr f` bonlrc`hbøo hlo f` h`fbm`m `mkhu`m` p`r` tlc`r mkhbsbloks knbhbkotks. Kstk prlhksl, kf mk tr`osnlrc`r fls m`tls ko bonlrc`hbøo, sk hlosbjuk utbfbz`oml akrr`cbkot`s quk prlvkk f` hbkohb` kst`mãstbh`, `fjuo`s mk f`s hu`fks `prkomkrà, ustkm, `cbjl kstumb`otk, ko kstk hursl.

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0.7 C@T@ HLOHKT][@F C`p` hlohkptu`f 0.- [obm`m 0 

Nukotk9 WBOHØO, Jkrcào. [obm`mks ]kholføjbh`s mk X`ot`omkr. 7401

0.8 @XTKH]LX JKOKW@FKX MK F@ KX]@MÃX]BH@  0.8.0 Fls nkoøckols. [o` mk f`s `pfbh`hbloks mk f` kst`mãstbh` ks mkshrbgbr kf hlcplrt`cbkotl mk fls nkoøckols ko fls quk sk botkrks`o fls skrks auc`ols, plr fl quk ks bcplrt`otk prkhbs`r quk sk kotbkomk, ko kst` hbkohb`, plr nkoøckols.  

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  [o nkoøckol ks hu`fqubkr c`obnkst`hbøo mk f`s `htbvbm`mks auc`o`s l mk f` o`tur`fkz` quk pukmk skr pkrhbgbml plr fls skotbmls l f` r`zøo. @fjuols kikcpfls mk nkoøckols slo fls sbjubkotks9 

  Kf hrkhbcbkotl mk uo` pf`ot`   Kf hlcplrt`cbkotl mkf hfbc`

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  F`s vkot`s plr pkrblml mk uo` kcprks`

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  F`s pkrslo`s, plr mã`, quk slo `nkht`m`s plr uo` konkrckm`m

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  Fls `hhbmkotks mk tràosbtl kko o mbnkrkotks fuj`rks mk uo` hbum`m

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  F` v`rb`hbøo ckosu`f mkf hlstl mk vbm`

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T`f`gr`s sboøobc`s mk nkoøckol slo9 suhksl, akhal l `hlotkhbcbkotl 0.8.7 Tlr quâ ols botkrks`o fls nkoøckols. Tlr cuhals cltbvls fls skrks auc`ols mksk`o plskkr bonlrc`hbøo slgrk kf hlcplrt`cbkotl mk mbvkrsls nkoøckols y p`r` kffl rk`fbz`o rkjbstrls slgrk kf kst`ml mk kstls nkoøckols ko mbnkrkotks clckotls l ksp`hbls. 

Xbkcprk quk sk` vb`gfk kxtr`kr m`tls mk uo nkoøckol, ks plsbgfk, utbfbz`oml `fjùo prlhksl, hlovkrtbr kstls m`tls ko bonlrc`hbøo y ks kst` bonlrc`hbøo f` quk ols pkrcbtk tlc`r mkhbsbloks knbhbkotks, ks mkhbr, kfkjbr f` `ftkro`tbv` càs n`vlr`gfk mkotrl mk uo` `cpfb` j`c` mk plsbgbfbm`mks.

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C`p` hlohkptu`f 7. ¼Tlr quâ ols botkrks`o fls nkoøckols<  

Nukotk9 WBOHØO, Jkrcào. [obm`mks ]kholføjbh`s mk X`ot`omkr. 7401

Kstls rkjbstrls l ckmbhbloks ckmbhbl oks jkokr`o mbvkrsls vlfùckoks mk m`tls y p`r` quk kstls m`tls sk hlovbkrt`o hlovbkrt `o ko bonlrc`hbø bonlrc`hbøoo sk mkgko pprlhks`r rlhks`r mk mbnkrkotks c`okr`s. [o` mk f`s nlrc`s hlcl sk pukmko tr`t`r fls m`tls p`r` kxtr`kr f` bonlrc`hbøo quk kffls hlotbkokoo ks utbfbz`oml f`s tâhobh`s kst`mãstbh`s. hlotbkok 0.8.8  Mk Mknbo nbobhb bhbøo øo mk kst`mãstbh`. Ks uo` hbkohb` quk kstumb` høcl mkgk kcpfk`rsk

bonlrc`hbøo p`r` n`hbfbt`r f` tlc` mk mkhbsbloks ko sbtu`hbloks pràhtbh`s quk sk c`obnbkst`o g`il bohkrtbmucgrk.

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  0.8.= Bcplrt`ohb` mk f` kst`mãstbh`. F` `htbvbm`m càs bcplrt`otk p`r` f`s pkrslo`s quk tr`g`i`o ko f`s lrj`obz`hbloks kcprks`rb`fks ks f` tlc` mk mkhbsbloks. M`ml kf kolrck `uckotl mk f` mbsplobgbfbm`m mk m`tls (jr`hb`s ` fls sbstkc`s mk bonlrc`hbøo), y m`m` f` hlcpfkibm`m hrkhbkotk mk f`s lpkr`hbloks kcprks`rb`fks, fls prlhksls mk mkhbsbøo sk vko slcktbmls ` prksbloks kxtr`lrmbo`rb`s. 

[o` mk f`s tâhobh`s càs v`fbls` quk `yum`o ko fls prlhksls mk tlc` mk mkhbsbloks ks f` Kst`mãstbh`. Kst`mãstb h`. Tlr fl quk ks bombspkos`gfk quk fls alcgrks y cuikrks quk mbrbjko lrj`obz`hbloks l quk mk `fjuo` c`okr` p`rtbhbp`o ko f` tlc` mk mkhbsbloks kstâo n`cbfb`rbz`mls hlo f`s tâhobh`s kst`mãstbh`s p`r` plmkr mktkrcbo`r huàoml sk pukmk kx`cbo`r uo prlgfkc` kxbstkotk ckmb`otk f` `pfbh`hbø `pfbh`hbøoo mkf `oàfbsbs kst`mãstb kst`mãstbhl. hl. 0.8.; Mbvbsbøo mk f` kst`mãstbh` F` Kst`mãstbh` sk mbvbmk ko mls jr`omks r`c`s9     F` Kst`mãstbh` Mkshrbptbv`

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  F` Bonkrkohb` Kst`mãst Kst`mãstbh` bh`

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C`p` hlohkptu`f 8. Hf`sbnbh`hbøo mk f` kst`mãstbh`  

Nukotk9 WBOHØO, Jkrcào. [obm`mks ]kholføjbh`s mk X`ot`omkr. 7401

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  0.8.> Kst`mãstbh` mkshrbptbv`. Xlo fls hlolhbcbkotls y câtlmls quk tr`t`o mk f` rkhlfkhhbøo, lrj`obz`hbøo y prkskot`hbøo oucârbh` y jrànbh` mk fls m`tls . 

Fls `oàfbsbs quk sk a`hko hlo f`s akrr`cbkot`s mk f` kst`mãstbh` mkshrbptbv` sk fbcbt`o, ùobh`ckotk, `f hloiuotl mk m`tls quk sk rkhlfkht`rlo. 0.8.: Bonkrkohb` kst`mãstbh`. Xlo fls hlolhbcbkotls y câtlmls quk pkrcbtko9  

  X`h`r hlohfusblo hlohfusbloks ks slgrk kf hlcplrt`cbkotl tlt`f mk uo nkoøckol g`sàomlsk

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ùobh`ckotk ko f` bonlrc`hbøo rkhlfkht`m` slgrk uo` p`rtk mk ksk cbscl nkoøckol. Kst`s hlohfusbloks sk lgtbkoko g`il bohkrtbmucgrk.   Kstbc`r kf hlcplrt`cbkot hlcplrt`cbkotl l nuturl mk uo nkoøckol

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0.8.1 N`sks mk uo` bovkstbj`hbøo kst`mãstbh`. F`s n`sks l p`sls quk sk mkgko bohfubr ko uo kstumbl kst`mãstbhl slo cuy v`rb`m`s y mkpkomko mk mbnkrkotks hbrhuost`ohb`s, t`fks hlcl, fls lgiktbvls quk sk prktkomko prktkomk o `fh`oz`r l kf hlotkxtl ko quk sk rk`fbz` f` bovkstbj`hbøo. @quã sk prkskot` uo` mk kst`s plsbgbfbm`mks 9 

0. Tf`ok`cbkotl   Nbo mk f` bovkstbj`hbøo

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  Mknbobr f` plgf`hbøo

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  [obm`m mk bovkstbj`hb bovkstbj`hbøo øo   O`tur`fkz` l hf`sk mk fls m`tls

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  Nukotks mk f` bonlrc`hbøo

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  Trlhkmbcbkotl p`r` rkhlfkht`r fls m`tls

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  Mbskðl mk bostruckotls

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7. Trksupukstl 8. Wkhlfkhhbøo mk fls m`tls =. Hrãtbh` y hlmbnbh`hbøo ;. ]`guf`hbøo, jrànbh`s y ckmbm`s 02

 

  >. @oàfbsbs k botkrprkt`hbøo F` n`sk mk pf`ok`cbkotl ks f` càs bcplrt`otk mk tlml kf prlhksl5 mk f` hlrrkht` kf`glr`hbøo y mks`rrlffl, mk f`s kt`p`s quk hlcploko kst` n`sk, mkpkomk f` h`fbm`m mk fls rksuft`mls quk sk lgtkoj`o. Kf nbo mk f` bovkstbj`hbøo sk rknbkrk `f rksuft`ml hlohrktl quk sk v` ` lgtkokr mkf kstumbl kst`mãstbhl. [su`fckotk sk nlrcuf` ko nlrc` mk uo` prkjuot` quk sk ff`c` Trkjuot` mk Bovkstbj`hbøo. Fls hlohkptls mk9 Tlgf`hbøo y [obm`m mk Bovkstbj`hbøo sk tr`t`rào ko kf sbjubkotk cømufl. ]lmls fls m`tls, quk sk rkhlfkht`o slgrk uo nkoøckol, sk pukmko hf`sbnbh`r gàsbh`ckotk ko mls h`tkjlrã`s9 m`tls mk o`tur`fkz` hu`fbt`tbv` y m`tls mk o`tur`fkz` hu`otbt`tbv`. Fls m`tls mk o`tur`fkz` hu`fbt`tbv` l m`tls hu`fbt`tbvls, slo fls quk sk rkjbstr`o ko nlrc` mk p`f`gr`s, t`fks hlcl, kf kst`ml hbvbf mk f`s pkrslo`s, f`s prlnksbloks u lnbhbls mk f`s pkrslo`s l kf obvkf kmuh`tbvl.

F`s nukotks mk bonlrc`hbøo mk mlomk sk pukmko lgtkokr fls m`tls slo mk mls hf`sks9   Nukotks mk bonlrc`hbøo prbc`rb`s

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  Nukotks mk bonlrc`hbøo skhuom`rb`s

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F`s nukotks mk bonlrc`hbøo slo prbc`rb`s hu`oml fls m`tls, quk sk prlhks`o, fls a`o lgtkobml, mbrkht`ckotk, fls rk`fbz`mlrks mkf kstumbl.

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  F`s nukotks mk bonlrc`hbøo slo skhuom`rb`s hu`oml fls m`tls, quk sk prlhks`o, sk a`o lgtkobml ` tr`vâs mk ltr`s pkrslo`s l kotbm`mks, hlcl plr kikcpfl, Kf G`ohl mk f` Wkpùgfbh`, Kf M@OK, f`s hàc`r`s mk hlckrhbl l hu`fqubkr ltrl kstumbl y` rk`fbz`ml. Kf prlhkmbcbkotl p`r` rkhlfkht`r fls m`tls sk rknbkrk ` f`s `htbvbm`mks quk sk v`o ` kikhut`r p`r` rkhlfkht`r kstls m`tls. Kst`s `htbvbm`mks pukmko skr9   F` lgskrv`hb lgskrv`hbøo øo mbrkht`

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  F`s kohukst`s quk pukmko skr pkrslo`fks l vbrtu`fks

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  F`s kotrkvbst`s bombvbmu`fks l jrup`fks

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  F` kxpkrbckot`hbø kxpkrbckot`hbøoo

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Kf mbskðl mk bostruckotls sk rknbkrk `f mbskðl mk fls slplrtks mlomk sk v`o ` rkjbstr`r fls m`tls, hlcl plr kikcpfl, kf mbskðl mk fls nlrc`tls p`r` rkjbstr`r f`s lgskrv`hbloks,, kf mbskðl mk f`s kohukst`s l f` fbst` mk tkc`s quk sk v`o ` tr`t`r lgskrv`hbloks ko uo` kotrkvbst kotrkvbst`` y f` nlrc` hlcl sk v`o ` rkjbstr`r f`s rkspukst`s u lpbobloks mkf kotrkvbst`ml. Kf prksupukstl sk rknbkrk ` f` kstbc`hbøo l hàfhufl mkf hlstl, mk f`s mbnkrkotks kt`p`s mkf kstumbl. F` rkhlfkhhbøo mk fls m`tls m`tls l tr`g`il mk h`cpl, ks f` kt`p` mlomk sk ``pfbh`o pfbh`o f`s kohukst`s, sk rkjbstr`o f`s lgskrv`hbloks l sk rk`fbz`o f`s kotrkvbst`s. F` hrãtbh` sk rknbkrk ` f` `prkhb`hbøo mk f` vkr`hbm`m, `utkotbhbm`m y pkrtbokohb` mk fls m`tls rkhlfkht`mls.

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  F` t`guf`hbøo, jrànbh`s y ckmbm`s sk rknbkrk ` fls prlhksls, ` tr`vâs mk fls hu`fks, fls m`tls sk hlovbkrtko ko t`gf`s, hu`mrls rksùckoks, jrànbh`s rkprkskot`tbv`s l oùckrls quk pkrcbt`o mkshrbgbr y hlcprkomkr kf nkoøckol quk sk kstà kstumb`oml.

@oàfbsbs k botkrprkt`hbøo ks f` kt`p` mlomk sk hlohrkt` kf nbo mk f` bovkstbj`hbøo, y` sk`, rksplombkoml ` f` prkjuot` mk bovkstbj`hbøo, mkshrbgbkoml kf nkoøckol ko kstumbl l s`h`oml `fjùo tbpl mk hlohfusbloks slgrk âf. Kstls `oàfbsbs pukmko tkokr mls tbpls mk `fh`ohk9   @oàfbsbs k botkrprkt`hbøo mmkshrbptbv kshrbptbvls9 ls9 hu`oml fls `oàfbsbs k botkrprkt`hbloks sk

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hbrhuoshrbgko ùobh`ckotk ` fls m`tls rkhlfkht`mls.   @oàfbsbs k botkrprkt`hbøo bonkrkohb`f9 hu`oml fls `oàfbsbs k botkrprkt`h botkrprkt`hbloks bloks sk

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kxtbkomko ` tlmls fls kfkckotls mk f` plgf`hbøo l hu`oml sk a`hko kstbc`hbloks slgrk kf hlcplrt`cbkotl nuturl mkf nkoøckol ko kstumbl. 0.= HLOHKT]LX G@XBHLX T`r` bobhb`r kf kstumbl mk f` kst`mãstbh`, sk rkqubkrk prkhbs`r kf sbjobnbh`ml, quk tbkoko ko kst` hbkohb`, bmk`s, p`f`gr`s y hlohkptls quk ko ltrls h`cpls l ko oukstr`s `htbvbm`mks hltbmb`o`s, tbkoko skotbmls quk v`o mksmk fbjkr`ckotk mbnkrkotks ` mb`cktr`fckotk lpukstls. 0.=.0 M`tl. Ko târcbols jkokr`fks uo m`tl ks uo rkjbstrl l `olt`hbøo quk sk a`hk mkf kst`ml mk uo nkoøckol ko uo clckotl mktkrcbo`ml. mktkrcbo`ml .

0.=.7 Hf`sbnbh`hbøo mk fls m`tls. Fls m`tls sk pukmko hf`sbnbh`r `tkombkoml ` su prlpb` o`tur`fkz` l `tkombkoml ` fls obvkfks mk ckmbhbøo, hlcl sk cukstr` ko f` sbjubkotk jrànbh`9 

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  C`p` hlohkptu`f =. Hf`sbnbh`hbøo mk fls m`tls  

Nukotk9 WBOHØO, Jkrcào. [obm`mks ]kholføjbh`s mk X`ot`omkr. 7401

0.=. 0.=.7. 7.0 0H Hf`sbnb f`sbnbh`hbøo h`hbøo mk fls m `tls plr su o `tur`fkz` M`tls Hu`fbt`tbvls l h`tkjørbhls 9 Xlo fls m`tls quk rkprkskot`o `trbgutls quk

plskko fls kfkckotls y sk kxprks`o ckmb`otk p`f`gr`s hlcl plr kikcpfl9   Kf hlflr mk fls lgiktls9 Wlil, vkrmk l `zuf

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  f` prlnksbøo mk f`s pkrslo`s9 kstumb`otk, h`rpbotkrl, `glj`ml

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  Kf kst`ml hbvbf mk f`s pkrslo`s9 Xlftkrl, h`s`ml, skp`r`ml

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  kf obvkf mk h`fbm`m mk uo prlmuhtl9 @hkpt`ml, rkha`z`ml

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  Kst`ml mk s`fum mk f`s pkrslo`s. Kxhkfkotk, gukol, bos`tbsn`htlrbl bos`tbsn`ht lrbl 78

 

  M`tls Hu`otbt`tbvls9 Xk kxprks`o ckmb`otk oùckrls y sk rknbkrko ` hlotkls mk

kfkckotls quk plskko mktkrcbo`m` h`r`htkrãstbh` l ` ckmbm`s quk sk rk`fbz`o slgrk fls kfkckotls quk sk lgskrv`o. Tlr kikcpfl9

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  Oùckrl mk kstumb`otks quk sk jr`mu`rlo kf skckstrk p`s`ml   Oùckrl mk prlmuhtls rkha`z`mls plr kf hlotrlf mk h`fbm`m ko uo fltk mk

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prlmuhhbøo   Oùckrl mk `hhbmkotks lhurrbmls ko `fjùo sbtbl mk f` hbum`m

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  Tksl mk f`s h`i`s quk tr`osplrt` uo h`cbøo

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  X`f`rbl mk fls kcpfk`mls mk uo` kcprks`

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  Km`m mk f`s pkrslo`s

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0.=. 0.=.7. 7.7 7H Hf`sbnb f`sbnbh`hbøo h`hbøo m k fls m`tls plr su o bvkf mk ckmbh ckmbhbøo bøo Obvkff m k ckmbhbøo Olcbo` Obvk Olcbo`f9f9   Fls v`flrks quk tlc`o fls m`tls slo p`f`gr`s quk

ol slo sushkptbgfks mk `fjuo` nlrc` mk lrmko`cbkotl. Tlr kikcpfl9   Hlflr mk fls gltloks mk uo` h`i`

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Gf`ohl

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Okjrl

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@zuf

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Kth.

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Trlnksbøo mk f` pkrslo`s quk `sbstko ` uo skcbo`rbl

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@mcbobstr`mlrks

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Hlot`mlrks

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Bojkobkrls

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Ltrls

 

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  Obvkff m k ckmbhbøo Lrmbo`f9 Fls v`flrks quk tlc`o fls m`tls slo p`f`gr`s quk slo Obvk

sushkptbgfks mk `fjuo` nlrc` mk lrmko`cbkotl. Kst`s p`f`gr`s bombh`o kf jr`ml ko quk sk tbkok f` h`r`htkrãstbh` quk sk kstà cbmbkoml. Tlr kikcpfl9

Kst`ml mk s`fum mk f`s pkrslo`s. Fls m`tls sk pukmko hf`sbnbh hf`sbnbh`r `r ko9 kxhkfkotk, gukol, `hkpt`gfk, mknbhbkotk y c`fl Kf kstr`tl slhb`f mk f`s pkrslo`s. Fls m`tls sk pukmko hf`sbnbh`r ko9 kstr`tl `ftl, kstr`tl ckmbl, kstr`tl g`il.

Obvkf mk ckmbhbøo mk botkrv`fl9 Ko kf obvkf mk ckmbhbøo lrmbo`f ol sk pukmk

kst`gfkhkr f` c`jobtum mk f`s mbnkrkohb`s kotrk fls v`flrks quk tlc`o fls m`tls. Tlr kikcpfl9 ol sk s`gk sb f` mbnkrkohb` quk a`y kotrk kf kst`ml mk s`fum kxhkfkotk y guko`, ks f` cbsc` quk a`y kotrk kf kst`ml mk s`fum mknbhbkotk y c`f`. Ko kf obvkf mk ckmbhbøo mk botkrv`fl fls m`tls slo oùckrls quk tbkoko kst`s h`r`htkrãstbh`s9 Fls m`tls sk kxprks`o ko oùckrls, plr fl t`otl, sk pukmko lrmko`r F` mbst`ohb` quk a`y kotrk botkrv`fls mk v`flrks ks f` cbsc` p`r` tlm` f` ksh`f` mk ckmbhbøo Kf hkrl ks uo v`flr `rgbtr`rbl quk ol sbjobnbh` `uskohb` tlt`f mk f` prkskohb` mk f` h`r`htkrãstbh` F` suc`, f` rkst` mk v`flrks y kf pprlckmbl rlckmbl mk v`flrks, tbkoko skotbml rk`f, pkrl, f` mbvbsbøo ol. Kikcpfl9 uo kstumb`otk lgtuvl ko f` prbckr` prukg` uo` olt` mk 8,; y ko f` skjuom` prukg` uo` olt` mk =,;. Tlr fl t`otl9  

Fk nuk ckilr ko f` skjuom` prukg` quk ko f` prbckr`

 

F` mbst`ohb` l mbnkrkohb`, quk a`y kotrk kf botkrv`fl mk 8,; ` =,; ks f` cbsc` quk a`y kotrk kf botkrv`fl mk 0,; ` 7,;  

[o` olt` mk hkrl ol qubkrk mkhbr quk ol s`gk `gslfut`ckotk o`m` mkf tkc` mk f` prukg` 7;

 

   

Kf prlckmbl mk f`s olt`s lgtkobm`s ko f`s mls prukg`s, =,4, tbkok skotbml rk`f

 

[o` olt` mk =,4 ol kqubv`fk `f mlgfk mk mkskcpkðl mk uo` olt` mk 77,4. ,4.

Obvkf mk ckmbhbøo mk r`zøo9  fls m`tls tbkoko f`s cbsc`s h`r`htkrãstbh`s mkf obvkf mk botkrv`fl, pkrl, `mbhblo`fckotk, kf hkrl sbjobnbh` `uskohb` `uskohb ` tlt`f mk f` h`r`htkrãstbh`

quk sk cbmk y f` mbvbsbøo l r`zøo kotrk mls m`tls tbkok skotbml rk`f.   Kikcpfl9 Kf pksl mk f`s h`i`s quk vbkoko mkotrl mk uo hlotkokmlr.



 

[o` h`i` quk pks` 84 ebfljr`cls pks` càs quk uo` h`i` quk pks` 04 ebfljr`cls

 

F` mbst`ohb` l mbnkrkohb` quk a`y kotrk kf botkrv`fl mk m`tls kotrk 84 y =4

 

ebfljr`cls ks f` cbsc` mbst`ohb` quk a`y kotrk 74 y 84 ebfljr`cls Hkrl ebfljr`cls qubkrk mkhbr `uskohb` tlt`f mk pksl

 

Kf pksl prlckmbl mk 7 h`i`s quk pks`o rkspkhtbv`ckotk, 74 y 84 ebfljr`cls, tbkok skotbml rk`f

 

[o` h`i` quk pks` 84 ebfljr`cls pks` kf mlgfk mk ltr` quk pks` 0; ebfljr`cls. (F` r`zøo kotrk 7 m`tls tbkok skotbml rk`f)

 

0.=.8 Kfkckotl . Ko jkokr`f, uo kfkckotl ks uo` p`rtk bombvbsbgfk mk uo tlml l uo

hlcplokotk bombvbsbgfk l gàsbhl mk uo hukrpl. Tkrl, ko kst`mãstbh` sk ff`c` kfkckotl ` f`s kotbm`mks quk tbkoko uo` l v`rb`s h`r`htkrãstbh`s huyl kst`ml ols botkrks` rkjbstr`r. Kf rkjbstrl mkf kst`ml mk kst`s h`r`htkrãstbh`s ks fl quk hlostbtuyk fls m`tls. Kstls kfkckotls pukmko skr bombvbmuls, lgiktls l suhksls. Fls bombvbmuls pukmko skr pkrslo`s l skrks vbvls `obc`fks l vkjkt`fks. Fls suhksls pukmko skr, plr kikcpfl, fls `hhbmkotks mk tràosbtl, fls kohukotrls mkplrtbvls, fls rkhlrrbmls quk rk`fbz` uo vkaãhufl l fls mã`s mkf `ðl

7>

 

 

Nbjur` 0. Hlohkptl mk Kfkckotl  

Kikcpfls mk kfkckotls    Ko uo` bovkst bovkstbj`hbøo bj`hbøo slgrk kf hlcplrt`cbkot hlcplrt`cbkotll mk fls s`f`rbls mk tr`g`i`mlrks



fls kfkckotls slo fls tr`g`i`mlrks (pkrslo`s), y f` h`r`htkrãstbh` h`r`htkrãst bh` quk sk lgskrv` ` h`m` kfkckotl ks kf v`flr mk su s`f`rbl.   Ko uo` bovkstbj`hbø bovkstbj`hbøo o slgrk hlcplrt`cbkotl mk f`s vkot`s



mk uo`

hlckrhb`fbz`mlr` fls kfkckotls plmrã`o skr f`s n`htur`s (uo lgiktl), y f` h`r`htkrãstbh` lgskrv`m` ks kf v`flr mk h`m` n`htur`.   ]`cgbâo, Ko uo` bovkstbj`hbøo bovkstbj`h bøo slgrk hlcplrt`cbkotl mk f`s vkot`s mk uo`



hlckrhb`fbz`mlr` hlckrhb`fbz` mlr` fls kfkckotls plmrã`o skr fls cksks 7:

(uo suhksl), y f`

 

  h`r`htkrãstbh` lgskrv`m` kf v`flr mk f`s vkot`s mk h`m` cks   Ko uo` bovkstbj`hbøo bovkstbj`h bøo slgrk fls `hhbmkotks mk tràosbtl fls kfkckotls slo fls



`hhbmkotks (uo suhksl), y f` h`r`htkrãstbh` lgskrv`m` plmrã` skr kf oùckrl mk pkrslo`s fksblo`m`s plr `hhbmkotk lgskrv`ml Fls nkoøckols sk prlmuhko hu`oml kf kst`ml mk f`s h`r`htkrãstbh`s lgskrv`m`s v`rã`, usu`fckotk, mk uo kfkckotl ` ltrl. 0.=.= Tlgf`hbøo. Ko kst`mãstbh` kf hlohkptl mk Tlgf`hbøo ks cuhal càs `cpfbl quk kf quk sk utbfbz` ko kf fkoju`ik hlrrbkotk. Ko kst` hbkohb`, hu`oml sk a`gf` mk Tlgf`hbøo ols rknkrbcls `9  

  ]lmls fls kfkckotls quk prkskot`o uo` h`r`htkrãs h`r`htkrãstbh` tbh` hlcùo



  Ks kf hloiuotl mk tlmls fls kfkckotls quk a`hko p`rtk mk uo` sbtu`hbøo quk sk



kstà kstumb`oml y slgrk f` hu`f sk botkot` s`h`r hlohfusbloks

0.=.; Hlcl sk mknbok uo` plgf`hbøo. F`s plgf`hbloks sk mkgko mknbobr hlo tlm` hf`rbm`m mk t`f c`okr` quk ol kxbst` hlonusbøo slgrk sb uo mktkrcbo`ml kfkckotl pkrtkokhk l ol ` f` plgf`hbøo. T`r` n`hbfbt`r kst` mknbobhbøo, ko cuhals h`sls, f`s p`f`gr`s quk f` hlcploko sk pukmko lrmko`r mk `hukrml ` f` sbjubkotk sbot`xbs9   ]LMLX(@X) + MKXHWBTHB MKXHWBTHBØO ØO M MKF KF KFK KFKCKO]L CKO]L + HLOMBHBØO WKX]WBH]B^@

Xbjobnbh` quk uo` mknbobhbøo mk plgf`hbøo mkgk kcpkz`r plr f` p`f`gr` ‖]lmls– l ‖]lm`s– skjubm` mk uo` mkshrbphbøo mkf kfkckotl quk sk kstà lgskrv`oml càs uo`

rkstrbhhbøo `f `fh`ohk mk f` p`f`gr` ]lmls(`s) Kikcpf Kik cpfl l Ol.0

71

 

 

Ko uo kstumbl mkf obvkf s`f`rb`f mk fls lpkr`rbls mkf skhtlr mk hlonkhhbloks mk f` hbum`m, uo` mknbobhbøo mk plgf`hbøo plmrã` skr f` sbjubkotk9

]lmls fls lpkr`rbls mkf skhtlr mk hlonkhhbloks mk f` hbum`m 0.=.> ]`c`ðl ]`c`ðl mk uo` plgf`hbøo. Ks kf oùckrl tlt`f mk kfkckotls quk hlcploko uo` plgf`hbøo, quk quk sk a` mknbobml prkvb`ckotk. Kf t`c t`c`ðl `ðl mk uo` plgf`hbøo sk sukfk rkprkskot`r plr f` fktr` O  Kikcpf Kik cpfl l Ol.7 Ol.799  

T`r` bombh`r quk uo` plgf`hbøo tbkok >:4 kfkckotls sk bombh` `sã9 O 3 >:4. 0.=.: Hf`sks mk plgf`hbloks. F`s plgf`hbloks sk mbvbmko ko mls hf`sks, tkobkoml ko hukot` su t`c`ðl9    Tlgf`hbloks nbobt`s



 Tlgf`hbloks bonbobt`s



0.=.:.0 Tlgf`hbloks Nbobt`s. Xlo f`s plgf`hbloks ` f`s hu`fks sk fks pukmko mktkrcbo`r nàhbfckotk kf oùckrl mk kfkckotls quk f`s hlcploko, ks mkhbr, su t`c`ðl. 

Kikcpf Kik cpfl l Ol.8 Ol.899

Xbtu`hbøo l nkoøckol9 F` km`m mk fls kstumb`otks mk f`s []X Tlgf`hbøo9 ]lmls fls kstumb`otks mk f`s []X ]bpl mk plgf`hbøo9 Nbobt`, plrquk nàhbfckotk sk pukmko hlot`gbfbz`r sus kfkckotls `humbkoml ` f` lnbhbo` mk f` bostbtuhbøo quk rkjbstr` kstls m`tls

72

 

 

0.=.:.7 Tlgf`hbloks bonbobt`s    Xlo f`s plgf`hbloks quk nãsbh` nãsbh`ckotk ckotk ks bcplsbgfk ouckr`rf`s l mktkrcbo`r su



t`c`ðl   Xlo f`s plgf`hbloks plgf`hbloks quk `uoquk sk pukmk mmktkrcbo`r ktkrcbo`r su t`c`ðl, ol ks



hlovkobkotk a`hkrfl plr r`zloks khloøcbh`s l mk tbkcpl

Kikcpf Kik cpfl l Ol.= Ol.=99

Xbtu`hbøo9 @hhbmkotks plr mã` ko uo hruhk mk h`ffks mk f` hbum`m Tlgf`hbøo9 ]lm`s fls mã`s cbkotr`s kxbst` kstk hruhk ]bpl mk plgf`hbøo9 Bonbobt`. Ks bcplsbgfk mktkrcbo`r huàotls kfkckotls tbkok kst` plgf`hbøo Kikcpf Kik cpfl l Ol.; Ol.;99

Xbtu`hbøo9 Oùckrl prlckmbl mk abils plr p`rki` mk uo g`rrbl mk f` hbum`m Tlgf`hbøo9 tlm`s f`s p`rki`s quk a`gbt`o ko kf g`rrbl ]bpl mk plgf`hbøo9 Bonbobt`. Ks cuy hlstlsl l mkc`om` cuhal tbkcpl mktkrcbo`r su t`c`ðl

0.=. 0.=.1 1H H`r`htkrãstbh`s `r`htkrãstbh`s lgskrv`gfks lg skrv`gfks ko u uo` o` plgf`hbø o C`p` hlo hlohkptu`f hkptu`f ;. Hf`sbnbh`hbøo mk f`s v`rb`gf v `rb`gfks ks kst`mãstbh`s

84

 

 

Nukotk9 WBOHØO, Jkrcào. [obm`mks ]kholføjbh`s mk X`ot`omkr. 7401

@ fls kfkckotls mk uo` plgf`hbøo plgf`hbøo sk fks lgskrv`o sus h`r`h h`r`htkrãstbh`s tkrãstbh`s l f` botkosbm`m hlo quk sk prkskot` uo` c`jobtum. Mk `hukrml hlo su hlcplrt`cbkotl f`s h`r`htkrãstbh`s quk sk lgskrv`o ko fls kfkckotls mk uo` plgf`hbøo sk pukmko hf`sbnbh`r ko hlost`otks l v`rb`gfks.

0.=.1.0 H`r`htkrãstbh`s hlost`otks . [o` h`r`htkrãstbh` ks hlost`otk hu`oml kf

v`flr quk prkskot` kst` h`r`htkrãstbh` ol v`rã` mk uo kfkckotl ` ltrl l v`rã` cuy plhl5 plr kikcpfl, kikcpfl, f` kst`tur` mk uo` ppkrslo` krslo` `muft` lgskrv`m` ko fls ùftbcls 74 cksks l f` prlnksbøo mk uo jr`mu`ml uobvkrsbt`rbl. 0.=.1.7 H`r`htkrãstbh`s v`rb`gfks

  Ks uo` h`r`htkrãs h`r`htkrãstbh` tbh` quk h`cgb` nrkhukotkckot nrkhukotkckotk k mk v`flr hu`oml sk lgskrv`



ko `fjuols l ko tlmls fls kfkckotls mk f` plgf`hbøo.   Ks uo sãcglfl quk ppukmk ukmk tlc`r mbvkrs mbvkrsls ls v`flrks mk mkotrl otrl mk uo hloiuotl



mktkrcbo`ml mk v`flrks quk rkhbgko kf olcgrk mk mlcbobl mk f` v`rb`gfk.(Xbjobnbh`ml c`tkcàtbhl) 80

 

 

F` kst`mãstbh` slf`ckotk kstumb` f`s h`r`htkrãstb h `r`htkrãstbh`s h`s v`rb`gfks Kst`s h`r`htkrãstbh`s v`rb`gfks, hlcùockotk mkolcbo`m`s v`rb`gfks, pukmko skr mk mls hf`sks9



  ^`rb`gfks ^`rb`gfks hu`fbt`tbv`s l h`tkjø h`tkjørbh`s rbh`s   ^`rb`gfks ^`rb`gfks hu`otbt`tb hu`otbt`tbv`s v`s



0.=. 0.=.2 2 ^` ^`rb`gfks rb`gfks hu`fbt`tbv h u`fbt`tbv `s l hh`tkjørbh`s `tkjørbh`s .

Xlo f`s quk mkshrbgko kf kst`ml mk

f` h`r`htkrãstbh` ùobh`ckotk ckmb`otk p`f`gr`s. Xk rknbkrko ` `trbgutls, hu`fbm`mks, `htbtumks l prknkrkohb`s mk fls kfkckotls quk sk kstào kstumb`oml. Kikcpf Kik cpfl l Ol.>9 

  F`s prlnksbloks u lhup`hbloks mk uo jrupl mk pkrslo`s9 @glj`ml, c`kstrl, p`o`mkrl, bojkobkrl, kth.

  Kf kst`ml hbvbf mk uo jrupl mk pkrslo`s9 Xlftkrl, h`s`ml, uobøo fbgrk, kth.



  Kf s`glr mk f`s o`r`oi`s mk uo` hlskha`9 mufhk, bosãpbml, àhbml



  Kf hlflr n`vlrbtl mk uo jrupl mk bombvbmuls bombvbmuls99 Gf`ohl, rlil, vkrmk, kth.



  T`s`tbkcpls mk uo jrupl mk kstumb`otks9 Mkplrtks, fkhtur`, rkuobloks slhb`fks slhb`fks,,



f`glrks c`ou`fks, kth.   F` h`fbm`m mmkk uo prlmuhtl9 Gukol, rkjuf`r l mknkhtulsl



Hlcl sk pukmk lgskrv`r, ko fls kikcpfls, h`m` uo` mk kst`s v`rb`gfks sk kxprks` ` tr`vâs mk mls l càs càs clm`fbm`mks l h`tkjlrã`s9 slftkrl, slftkr l, h`s`ml, uobøo fbgrk5 gukol, rkjuf`r, mknkhtulsl. Fls m`tls quk sk rkjbstr`o hu`oml f`s v`rb`gfks slo hu`fbt`tbv`s l h`tkjørbh`s hlrrksplomko ` f` h`otbm`m l prlplrhbøo mk kfkckotls quk h`ko mkotrl mk h`m` h`tkjlrã` quk tlc` f` v`rb`gfk, plr kikcpfl9 kf oùckrl mk `glj`mls l mk c`kstrls,

87

 

  kf oùckrl mk bombvbmuls quk prknbkrko kf hlflr gf`ohl, f` prlplrhbøo mk prlmuhtls mknkhtulsls. F`s v`rb`gfks h`tkjørbh`s sk pukmko ` su vkz sugmbvbmbr ko v`rb`gfks olcbo`fks y v`rb`gfks lrmbo`fks. 0.=.2.0 ^`rb`gfks Olcbo`fks . Xlo f`s quk ol tbkoko uo` nlrc` p`rtbhuf`r mk

lrj`obz`r sus h`tkjlrã`s. Tlr kikcpfl, ol kxbstk uo` nlrc` hlcùo mk lrmko`r fls hlflrks l kf kst`ml hbvbf mk f`s pkrslo`s. 0.=.2.7 ^`rb`gfks lrmbo`fks .

Hu`oml kxbstk uo` nlrc` hlcùo mk lrj`obz`r f`s

h`tkjlrã`s quk tlc` f` v`rb`gfk. Tlr kikcpfl9 f`s clm`fbm`mks hlcl sk pukmk kxprks`r f` h`fbm`m mk uo prlmuhtl sk pukmko lrmko`r hlcl gukol, rkjuf`r, mknkhtulsl l `f hlotr`rbl, ko mknkhtulsl, rkjuf`r, gukol. FF`s `s h`tkjlrã`s hlo f`s quk sk h`fbnbh` kf skrvbhbl quk prkst` uo` KTX sk pukmko lrmko`r hlcl pâsbcl, c`fl, rkjuf`r, gukol l kxhkfkotk.

0.=.04 ^`rb`gfks hu`otbt`tbv`s . Xlo f`s quk sk mkshrbgko plr ckmbl mk oùckrls,

plr kikcpfl, f` km`m mk fls kcpfk`mls mk uo` kcprks`, f`s pkrslo`s quk vbsbt`o plr mã` uo cuskl, fls s`fmls mk f`s hukot`s plr hlgr`r mk uo` kcprks`, kf pksl mk fls p`quktks quk clvbfbz` uo` kcprks` tr`osplrt`mlr`, kf oùckrl mk vkaãhufls quk vkomk uo hlohksblo`rbl, kth. `s v`rb`gfks hu`otbt`tbv`s sk pukmko hf`sbnbh`r, t`cgbâo, ko mbshrkt`s l hlotbou`s9 0.=. 0.=.04 04.0 .0 ^` ^`rb`gfks rb`gfks hu`otb t`tbv`s mbs mbshrkt`s hrkt`s . Xlo f`s quk ùobh`ckotk pukmko tlc`r

v`flrks kotkrls t`fks hlcl kf oùckrl mk vkaãhufls quk vkomk uo hlohksblo`rbl l kf oùckrl mk pkrslo`s quk `sbstko ` uo` s`f` mk hbok. 0.=. 0.=.04 04.7 .7 ^` ^`rb`gfks rb`gfks hu`otb hu`otbt`tbv`s t`tbv`s hlo hlotbo tbou`s. u`s. Xlo f`s quk sk rknbkrko ` ckmbhbloks

mk c`jobtumks nãsbh`s l ` h`r`htkrãstbh`s `prkhb`gfks ko uobm`mks clokt`rb`s y 88

 

  `mcbtko v`flrks nr`hhblo`rbls l mkhbc`fks t`fks hlcl kf pksl mk fls p`quktks quk clvbfbz` uo` tr`osplrt`mlr`, fls s`fmls mk f`s hukot`s mk `alrrl mk uo` kotbm`m nbo`ohbkr` l kf tbkcpl quk mur` kf rkhlrrbml mk uo gus urg`ol.

0.=. 0.=.04 04.8 .8 ^` ^`rb`gfks rb`gfks hu`otb t`tbv`s h`tkjør h`tkjørbh`s bh`s . Hu`oml sk qubkrk n`hbfbt`r kf c`okil

mk fls m`tls l `uckot`r f` hlcprkosbøo mk uo nkoøckol, f`s v`rb`gfk hu`otbt`tbv`s sk pukmko hlovkrtbr ko h`tkjørbh`s, hlcl hu`oml f`s pkrslo`s quk cbmko ckols mk 0.;4 cktrls sk hf`sbnbh`o hlcl mk kst`tur` pkqukð`, f`s pkrslo`s quk cbmko kotrk 0.;4 cktrls y ckols mk 0.:4 sk hf`sbnbh`o hlcl mk kst`tur` ckmb`o` y f`s pkrslo`s quk cbmko 0.:4 cktrls l càs sk hf`sbnbh`o hlcl mk kst`tur` `ft`.

0.=.00 Hkosl . Ks hu`oml sk lgskrv` y rkjbstr` kf kst`ml mk uo` h`r`htkrãstbh`

kx`cbo`ml ` tlmls fls kfkckotls mk uo` plgf`hbøo. Fls hkosls r`r` vkz sk rk`fbz`o mkgbml `f tbkcpl quk mkc`om`o y ` f` h`otbm`m mk rkhursls quk okhksbt`o plr fl quk sk rkhurrk ` tlc`r m`tls mkf kst`ml mk f` v`rb`gfk ko `fjuols mk fls kfkckotls mk f` plgf`hbøo. 0.=.07 Cukstr`.  Ks hu`oml sk lgskrv` y rkjbstr` kf kst`ml mk uo` h`r`htkrãstbh` h`r`htkrãs tbh`

v`rb`gfk kx`cbo`ml ` uo` p`rtk mk fls kfkckotls quk pkrtkokhko ` uo` plgf`hbøo. F`s cukstr`s mkgko skr rkprkskot`tbv`s y p`r` kstl sk rkqubkrk quk f`s h`r`htkrãstbh`s mk f` plgf`hbøo kstâo rkprkskot`m`s ko f` cukstr`, ko f` cbsc` prlplrhbøo ko quk kstào bohfubm`s ko f` plgf`hbøo. 0.=.07 0.= .07.0 .0 ]`c`ðl mk f` cukstr`. cu kstr`.   Ks kf oùckrl mk kfkckotls quk hlcploko f`

cukstr`. Xk sukfk bombh`r hlo f` fktr` o.

Kikcpf Kik cpfl l Ol.: Ol.:99  

8=

 

  T`r` bombh`r quk uo` cukstr` tbkok 8;4 kfkckotls sk bombh` `sã9 o 3 8;4 0.=.08 0.= .08 T`ràcktrl . Ks kf rksuft`ml mk uo` ckmbm` l hàfhufl quk sk a`hk utbfbz`oml

fls m`tls rkf`hblo`mls hlo kf v`flr quk tlc` uo` h`r`htkrãstbh` v`rb`gfk hu`oml sk lgskrv`o tlmls fls kfkckotls mk uo` plgf`hbøo, ks mkhbr, hu`oml hu`om l sk a`hk uo hkosl. Tlr kikcpfl, f` km`m prlckmbl mk fls obðls qquk uk hurs`o prbckr jr`ml, kstk `ðl, ko tlm`s f`s kshukf`s lnbhb`fks mk f` hbum`m. Kf p`ràcktrl sbkcprk ks uo v`flr hlost`otk.

ut bfbz`oml 0.=.0= Kst`mãstbhl. Ks kf rksuft`ml mk uo` ckmbm` l hàfhufl quk sk a`hk utbfbz`oml fls m`tls rkf`hblo`mls hlo kf v`flr quk tlc` uo` h`r`htkrãstbh` v`rb`gfk hu`oml sk lgskrv`o `fjuols mk fls kfkckotls mk uo` plgf`hbøo, l sk`, uo` cukstr`. Tlr kikcpfl, f` km`m prlckmbl mk fls obðls mk prbckr jr`ml mk `fjuo`s kshukf`s lnbhb`fks mk f` hbum`m kshljbm`s `f `z`r. Kf kst`mãstbhl ks uo v`flr quk v`rã` mk cukstr` ko cukstr`  cukstr` 

. 0.=.0; ]bpls mk kstumbls kst`mãstbhls.

Fls kstumbls kst`mãstbhls pukmko skr

kxpkrbckot`fks y mk lgskrv`hbøo.

Ko fls kstumbls kst`mãstbh kst`mãstbhls ls kxpkrbckot`fks kf bovkstbj`mlr hlotrlf` l c c`obpuf` `obpuf` uo` l v`rb`s v`rb`gfks hlo kf nbo mk mktkrcbo`r su hlcplrt`cbkotl ko mmktkrcbo`m`s ktkrcbo`m`s hlombhbloks. Ko fls kstumbls kst`mãstbhls mk lgskrv`hbøo kf bovkstbj`mlr rkjbstr` kf kst`ml mk f` h`r`htkrãstbh` v`rb`gfk quk fk botkrks` sbo kikrhkr obojuo` bonfukohb` slgrk kff`. Kf kstumbl kst`mãstbhl mk lgskrv`hbøo càs hlcùo ks f` kohukst`. 0.=.0> [obm`m mk lgskrv`hbøo l mk bovkstbj`hbøo.   Xk ff`c` [obm`m mk

Lgskrv`hbøo l mk Bovkstbj`hbøo ` `fjuol mk fls sbjubkotks hlohkptls9 8;

 

 

  @f olcgrk jkoârbhl, quk sk fk m` ` fls kfkckotls huy` h`r`htkrãst h`r`htkrãstbh` bh` sk kstà



rkjbstr`oml   @ f` kotbm`m quk sk bovkstbj` mk f` quk sk rkhlfkht`o fls m`tls





  @f slplrtk mk mlomk sk kxtr`ko fls m`tls

0.=.0: Kst`mãstbh`s Ks hu`fqubkr hloiuotl lrmko`ml mk m`tls hlcl plr kikcpfl f`s kst`mãstbh`s mk uo tlrokl mk nùtglf, f`s kst`mãstbh`s mk vkot`s mk uo` kcprks` l f`s kst`mãstbh`s mk `hhbmkotks  

0.=.01 Kikrhbhbls rksukftls  Kikrhb Kik rhb hbl Ol.0

Xk kohukst`rlo ` 744 pkrslo`s kshljbm`s `f `z`r kotrk tlm`s f`s pkrslo`s quk vbsbt`rlo uo hkotrl hlckrhb`f mk f` hbum`m, prkjuot`oml fl sbjubkotk9

  ¼Puâ mã` mk f` skc`o` prknbkrk p`r` vbsbt vbsbt`r `r kf hkotrl hlckrhb`f<



  ¼Wk`fbz` `fjuo` hlcpr` h`m` vkz quk vbsbt` kkff hkotrl hkotrl hlckrhb`f< hlckrhb`f<



  ¼Huàoml rk`fbz` `fjuo` hlcpr` ` quâ v`flr ppukmk ukmk `shkomkr kst` hlcpr`<



 

¼Huàfks slo fls kfkckotls mk kstk kstumbl<   Mknbo` f` plgf`hbøo ko kstumbl  

¼Mk quâ tbpl ks kst` plgf`hbøo<

 

¼Huàf ks f` cukstr` mk kstk kstumbl<

 

¼Huàf ks kf t`c`ðl mk kst` cukstr`<

 

¼Huàf ks kf tbpl kx`htl mk h`m` uo` mk f`s v`rb`gfks mkf kstumbl<

 

¼Huàf ks kf obvkf mk ckmbhbøo mk fls m`tls `slhb`mls `slh b`mls ` h`m` uo` mk f`s v`rb`gfks mk kstumb`m`s<

 

¼Huàfks slo f`s h`tkjlrã`s mk h`m` uo` mk f`s v`rb`gfks hu`fbt`tbv`s< 8>

 

   

¼Høcl sk pukmko h`tkjlrbz`r h`m` uo` mk f`s v`rb`gfks hu`otbt`tbv`s<

 

Xã kf v`flr cãobcl mk hlcpr`, kohlotr`ml ko kf kstumbl nuk mk $04.444 ¼Høcl sk ff`c` ko kst`mãstbh` ` kstk v`flr<

 

¼Puâ hlcplrt`cbkotl pukmk tkokr kf v`flr mkf puotl `otkrblr, huàoml sk tlcko

 

ltr`s cukstr`s< ¼Xk rk`fbzø uo hkosl l uo cukstrkl<

 

¼Puâ tbpl mk kstumbl sk rk`fbzø<

 

Xlfuhbøo

 

F`s pkrslo`s

 

]lm`s f`s pkrslo`s quk vbsbt`o ksk hkotrl hlckrhb`f

 

Bonbobt`

 

F`s 744 pkrslo`s kshljbm`s

 

o 3 744

 

Mã` mk f` skc`o` quk prknbkrk p`r` vbsbt`r kf hkotrl hlckrhb`f ^`rb`gfk lrmbo`f

¼Wk`fbz` `fjuo` hlcpr` h`m` vkz quk vbsbt` kf hkotrl hlckrhb`f<

  ^`rb`gfk

olcbo`f ^`flr mk f` hlcpr` ^`rb`gfk hlotbou`  

Mã`s mk f` skc`o`9 Fuoks, C`rtks, Cbârhlfks, Iukvks, ^bkroks, Xàg`ml, Mlcbojl

Wk`fbz` `fjuo` hlcpr`9 Xã, Ol  

^`flr mk f` hlcpr`, plr mk $04.444 ` $0;.4444 kikcpfl9

mk $0;.4444 ` $74.4444 mk $74.4444 ` $7;.444, kth

`)

Kst`mãstbhl

g)

Hlcplrt`cbkotl v`rb`gfk

h)

[o cukstrkl

m)

[o kstumbl lgskrv`hblo`f

8:

 

 

Kikrhb Kik rhb hbl Ol.7

F` hllpkr`tbv` mk `alrrl y hrâmbtl ‖HLLTKWHWÂMB]L–, kohukstø ` tlmls sus :;4 `nbfb`mls, prkjuot`oml fl sbjubkotk9   ¼Huàotl tbkcpl a`hk quk kstà `nbfb`ml ` f` hllpkr`tbv`< 

  ¼Huàotls hrâmbtls a` slfbhbt` slfbhbt`ml ml ko kf ùftbcl `ðl<



  H`fbnbquk mk 0 ` ; kf skrvbhbl quk rkhbgk mk f` hllpkr`tbv`, mlomk 0 ks pâsbcl, 8



ks rkjuf`r y ; ks kxhkfkot kxhkfkotk. k. `)

¼Huàfks slo fls kfkckotls mk kstk kstumbl<

g)

Mknbo` f` plgf`hbøo ko kstumbl

h)

¼Mk quâ tbpl ks kst` plgf`hbøo<

m)

¼Xk rk`fbzø uo hkosl l uo cukstrkl<

k)

¼Huàf ks kf t`c`ðl mk f` plgf`hbøo<

n)

¼Huàf ks kf tbpl kx`htl mk h`m` uo` mk f`s v`rb`gfks mkf kstumbl<

j)

¼Huàfks slo f`s h`tkjlrã`s mk h`m` uo` mk f`s v`rb`gfks hu`fbt`tbv`s<

a)

¼Høcl sk pukmko h`tkjlrbz`r h`m` uo` mk f`s v`rb`gfks hu`otbt`tbv`s<

b)

Xã hlcl càxbcl fls `nbfb`mls a`o slfbhbt`ml ; hrâmbtls, ko kf ùftbcl `ðl,

¼Høcl sk ff`c` ko kst`mãstbh` ` kstk v`flr<  i)

¼Puâ hlcplrt`cbkotl tbkok kf v`flr mkf puotl `otkrblr<

e)

¼Puâ tbpl mk kstumbl sk rk`fbzø<

Xlfuhbøo `)

Fls `nbfb`mls

g)

]lmls fls `nbfb`mls ` f` hllpkr`tbv` HLLTKWHWÂMB]L

h)

Nbobt`

m)

[o hkosl

k)

O 3 :;4

n)

]bkcpl mk `nbfb`hbøo  Hlotbou` Hrâmbtls slfbhbt`mls  Mbshrkt` H`fbnbh`hbøo mkf skrvbhbl  Lrmbo`f 81

 

  j)

a)

H`fbnbh`hbøo mkf skrvbhbl9 0, 7, 8, =, ;

]bkcpl mk `nbfb`hbø `nbfb`hbøo, o, plr kikcpfl

mk 4 ` 7 `ðls mk 7 ` = `ðls mk = ` > `ðls, kth.

b)

Hrâmbtls slfbhbt`mls, plr kikcpfl9

mk 4 ` 0 hrâmbtls mk 7 ` 8 hrâmbtls mk = ` ; hrâmbtls, kth.

 i)

T`ràcktrl

e)

Ks uo` hlost`otk

f)

[o kstumbl lgskrv`hblo`f

82