Coletanea - Probabilidades - Versão 2
October 4, 2022 | Author: Anonymous | Category: N/A
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@ouohmfki ‘ Hib`tço`f k` Urigfgmbmkfk`s
Urigfgmbmkfk`s ` Hingmoftørmf • Nft`nætmhf F ‘ 67¼ foi
Nft`nætmhf F ‘ foi Urigfgmbmkfk`s ` Hingmoftørmf
•
¼
6 Hæbhubi Hingmoftørmi. Urigb`nfs k` Hiotfc`n . Pnf
r`vmstf k` nüsmhf grmtçomhf t`v` f momhmftmvf k` hrmfr un moquírmti ofhmiofb k` dirnf f sfg`r qufb í f ipmomèi kis afgmtfot`s oi W`moi Pomki r`bftmvfn`ot` f qufb hiosmk`rfn s`r f n`bair gfokf grmtçomhf k` tikis is t`npis. Pn hirr`spiok`ot` k`ssf r`vmstf `n Nfoha`st`r sthiu r`spiosæv`b pir dfz`r i moquírmti f 61 p`ssifs. I hirr`spiok`ot` t`n kims kmfs pfrf igt`r fs r`spistfs ` pik`, oi næxmni, r`hiba`r f r`spistf k` 65 p`ssifs pir kmf. K` qufotfs dirnfs kmstmotfs pik` i hirr`spiok`ot` kmstrmgumr is moquírmtis p`bis kims kmfs9 (F) ;1 47 475 5
(G) 684684
(H) 6;0 6;0 145
(K) ;51 ;51 ;51
. Hiosmk`r`
tikis is oün`ris k` s`ms fbcfrmnis qu` hiotín `xftfn`ot` kims fbcfrmsnis 5, kims fbcfrmsnis 0 ` kims fbcfrmsnis 4. Vufotis k`ss`s oün`ris sèi nübtmpbis k` 09 (F) ;7 (F) ;7
(G) 45 (G) 45
(H) (H) 1; 1;
(K) (K) 7;5 7;5
. F
ípihf k` 7575 k` Dørnubf 6 nfrhfræ i 35 ¼ fomv`rsærmi kf prmn`mrf ípihf k` Dørnubf 6. Tèi hinp`tmr vmot` pmbitis k` k`z `qumpfs `qumpfs kmd`r`ot`s. I grmtçomhi grmtçomhi Bfoki Oirrms í un kis quftri quftri pmbitis grmtçomhis grmtçomhis qu` hinp`tmrèi of ípihf k` 7575 k` Dørnubf 6.
Tfm s`r `shibamki un crupi k` trìs pmbitis pfrf pfrf unf `otr`vmstf `otr`vmstf k` fot`vmsèi kf ípihf. W`bftmvfn`ot W`bftmvfn`ot`` f `ssf `shibaf sfg`-s` qu`< • i
crupi k`v`ræ s`r hiostmtuîki pir, p`bi n`ois, un pmbiti grmtçomhi:
• hfsi
i Bfoki Oirrms dfãf pfrt` ki crupi, `otèi o`oaun iutri pmbiti grmtçomhi pik`ræ dfz`r pfrt` ki crupi.
O`stfs hiokmãð`s, qufotis crupis kmstmotis pik`n s`r dirnfkis pfrf dfz`r f `otr`vmstf9 (F) 07=
(G) 11=
(H) 6571
(K) 651=
Hmohi . Hmohi
fnmcis pbfo`f pbfo`frfn rfn unf vmfc`n vmfc`n f Gukfp`s Gukfp`st` t` pfrf i v`rèi. v`rèi. Oi fvmèi, is fnmcis fnmcis vèi `stfr `stfr s`otfkis s`otfkis of n`snf n`snf stbf. O`oaun iutri pfssfc`mri s`otfr-s`-æ o`ssf stbf. F hiostcurfãèi k` fss`otis k`ssf stbf í 8-;-8, msti í, kims crupis bft`rfms k` 8 fss`otis ` un crupi h`otrfb k` ; fss`otis.
i r m ` r r ` u C b ` u c m N i o u O •
n i h . t f n s m f n b f o m s
K` qufotfs nfo`mrfs kmstmotfs pik`n is hmohi fnmcis s`otfr-s` o`ssf stbf k` dirnf f qu` `xftfn`ot` trìs k`b`s stqu`n s`otfkis oi crupi h`otrfb9 (F) 855
Hiosmk`r` . Hiosmk`r`
(G) 8455
(H) 3755
(K) ;8 75 755 5
tikis is oün`ris oün`ris ofturfms ofturfms k` hmohi fbcfrmsnis. fbcfrmsnis.
K`st`s oün`ris, qufotis tìn `xftfn`ot` `xftfn`ot` trìs fbcfrmsnis fbcfrmsnis 1 ` sèi n`oir`s qu` ;5 5559 9 (F) 651
(G) 675
(H) 735
(K) 855
•
= 6 5 7
©
6
Urigfgmbmkfk`s ` Hingmoftørmf • Nft`nætmhf F ‘ 67¼ foi
. Pnf
`npr`sf t`hoibøcmhf pirtucu`sf `npr`cf 705 p`ssifs ois s`us `shrmtørmis `n Uirtucfb ` @stfkis Pomkis kf Fnírmhf. F hinmssèi `x`hutmvf kf `npr`sf í hiostmtuîkf pir 66 p`ssifs, `otr` fs qufms ; vmh`-pr`smk`ot`s.
Oi lfotfr k` Oftfb kf `npr`sf vfm s`r tmrfkf unf diticrfstf å hinmssèi `x`hutmvf `n qu` is s`us n`ngris `stfrèi kmspistis bfki f bfki. K` qufotfs dirnfs pik` f hinmssèi `x`hutmvf s` kmspûr k` dirnf f oèi `xmstmr`n vmh`-pr`smk`ot`s `n bucfr`s hios`hutmvis ` i H@I kf `npr`sf ihupfr un bucfr ois `xtr`nis9
. I
høkmci ki hfrtèi k` nubtmgfohi ki Kfvmk í hiostmtuîki pir ; fbcfrmsnis k` 5 f =.
I høkmci ki s`u hfrtèi t`n kims fbcfrmsnis pfr`s mcufms, s`oki qu` is r`stfot`s kîcmtis sèi kmd`r`ot`s k`st`s übtmnis ` `otr` sm. Vufotiss høkmcis Vufoti høkmcis `xmst`n `xmst`n o`stfs hiokmãð`s9
. Pn
crupi k` k`z fnmcis dim f un pfrqu` k` ftrfãð`s ftrfãð`s.. Ounf kfs ftrfãð`s ftrfãð`s k`ss` n`sni pfrqu` pfrqu` dim p`kmki fi crupi qu` `shiba`ss` un k` kims hfnmoais (F iu G), s`oki qu` hfkf hfnmoai fknmtmf s`ms p`ssifs oi næxmni. K` qufotfs nfo`mrfs pûk` i crupi kmspir is s`us `b`n`otis p`bis kims hfnmoais9
. Pn
crupi k` k`z fnmcis hiostmtuîki pir imti rfpfz`s ` s`ms rfpfrmcfs.
Is fnmcis vèi kmstrmgumr-s` pir kufs stbfs hin imti bucfr`s hfkf, s`oki qu` ounf kfs stbfs s`otfr-s`-èi s`ms n`ngris ki crupi ` of iutrf s`otfr-s`-èi is r`stfot`s. Xfg`-s` fmokf qu` fs rfpfrmcfs sthfrèi mcufbn`ot` kmstrmguîkfs p`bfs kufs stbfs. @shr`vf unf `xpr`ssèi qu` p`rnmtf k`t`rnmofr i oün`ri k` nfo`mrfs kmstmotfs qu` is n`ngris ki crupi pik`n kmstrmgumr-s` kmstrmg umr-s` p`bfs kufs stbfs9
. Hiosmk`r`
un crupi k` k`z fnmcis hiostmtuîki pir s`ms rfpfz`s ` quftri rfpfrmcfs.
Fpøs t`r`n fssmstmki f un `sp`tæhubi, luotfrfn-s` fi crupi o rfpf rfpfrmc rmcfs fs pfrf mr f un gfr. gfr. K` dirnf dirnf f qu` tikis tikis is n`ngris ki crupi puk`ss`n mr pfrf i gfr dim o`h`ssærmi hafnfr un tæxm. Xfg`-s` qu`kmssi, quftri p`ssifs k` tæxm i gfr,iss`oki qu` i oün`ri k` rfpfz`s k` rfpfrmcfs qu` vèi oi tæxm í mcufb. Ufrf fbín i Kfvmk ` imrèi Lièi, qu` ftí b`vfrfn s`us hfrris, oèi pik`rèi mr oi`tæxm. Xfg`oki qu` `xmst`n 735 dirnfs kmd`r`ot`s k` s`b`hmiofr is n`ngris ki crupi qu` vèi oi tæxm, k`t`rnmo` qufotfs rfpfrmcfs s` luotfrfn fi crupi å sfîkf ki `sp`tæhubi.
. Hiosmk`r`
unf turnf k` kíhmni s`cuoki foi hiostmtuîkf pir 6; rfpfz`s ` 65 rfpfrmcfs.
Pnf kfs sfbfs iok` f turnf t`n fubfs í hinpistf pir 0 stbfs hin 0 n`sfs mokmvmkufms hfkf. @shr`vf f `xpr`ssèi qu` p`rnmt` hfbhubfr i oün`ri k` dirnfs kmd`r`ot`s qu` is fbuois kf turnf s` pik`n kmspir o`stf sfbf, sfg`oki qu` f prmn`mrf stbf k`v`ræ s`r ihupfkf pir trìs rfpfz`s ` kufs rfpfrmcfs.
i r m ` r r ` u C b ` u c m N i o u O •
Hiosmk`r` . Hiosmk`r`
tikis is oün`ris oün`ris ofturfms ofturfms k` hmohi fbcfrmsnis. fbcfrmsnis.
K`st`s oün`ris, qufotis tìn `xftfn`ot` `xftfn`ot` kims fbcfrmsnis fbcfrmsnis 5 ` kims fbcfrmsnis 6 9 (F) 6;; 7
(G) 7;5
(H) =45
(K) 8;04
n i h . t f n s m f n b f o m s •
= 6 5 7
©
Urigfgmbmkfk`s ` Hingmoftørmf • Nft`nætmhf F ‘ 67¼ foi
. Hiosmk`r`
un crupi k` kiz` fnmcis hiostmtuîki pir imti rfpfrmcfs ` quftri rfpfz`s, `otr` is qufms `stèi i Fotøomi `
i Tfshi. Is fnmcis k`hmkmrfn dirnfr kufs `qumpfs, F ` G . F `q `qum umpf pf F s`ræ hinpistf pir kufs p`ssifs, ` f `qumpf G s`ræ hinpistf hinpis tf pir trìs p`ssifs. p`ssifs. Xfg`-s` qu` f `qumpf F í hiostmtuîkf pir p`ssifs ki n`sni s`xi, ` f `qumpf G t`ræ k` s`r hiostmtuîkf pir p`ssifs kis kims s`xis. K` qufotfs dirnfs pik`rèi is fnmcis kmstrmgumr-s` p`bfs kufs `qumpfs9
. Hiosmk`r`
un crupi k` s`ms fnmcis hiostmtuîki p`bi Fotøomi, i Cumba`rn`, i Ouoi, i Wikrmci, i [inæs ` i Tfshi.
Is s`ms fnmcis vèi f un gfr ` t`rèi k` s` kmspûr ounf n`sf hin imti bucfr`s. Fs hfk`mrfs `stèi kmspistfs k` niki qu` `xmst`n kufs stbfs k` quftri hfk`mrfs. K` qufotfs nfo`mrfs pik`n is fnmcis s` kmspûr, sfg`oki qu` i Fotøomi sthfræ s`otfki fi bfki ki Cumba`rn`, ` i [inæs sthfræ å dr`ot` ki Tfshi9 . Hiosmk`r`
un sfhi hin qumoz` gibfs fp`ofs kmstmocuîv`ms p`bf hir< k`z fnfr`bfs ` hmohi fzums. 0 \
Of Dmcurf fi bfki `stæ r`pr`s`otfki un tfgub`mri hin vmoti ` hmohi hfsfs. Ur`t`ok`-s` hibihfr o`st` tfgub`mri fs qumoz` gibfs ki sfhi, k` dirnf f qu` hfkf gibf ihup` unf ` unf sø hfsf.
;
f
Hfkf dfh` ki prmsnf vfm s`r hibirmkf hin unf üomhf hir.
`
F @
G
D x
•
k
K
K` qufotfs dirnfs kmd`r`ot`s s` pik` pmotfr i prmsnf9
n i h . t f n s m f n b f o m s
h
z
H
Xfg`-s` qu` i prmsnf k`v` s`r pmotfki k` dirnf f qu` `xftfn`ot` kufs dfh`s s`lfn pmotfkfs kf n`snf hir, ` fs r`stfot`s trìs dfh`s s`lfn pmotfkfs hin hir`s kmd`r`ot`s `otr` sm.
. Hiosmk`r`
g
oun r`d`r`ohmfb i.o Ixyz , i prmsnf trmfocubfr r`ti Z FGHK@D ^ r`pr`s`otfki of Dmcurf fi bfki.
Kmspð`-s` k` imti hir`s kmd`r`ot`s pfrf hibirmr fs hmohi dfh`s ki prmsnf ZFGHK@D ^.
i r m ` r r ` u C b ` u c m N i o u O
\
8 \ \ \\\ 7 \ \ 6 \ \ \
K` qufotfs nfo`mrfs kmd`r`ot`s í pissîv`b kmspir fs qumoz` gibfs, k` tfb dirnf qu` unf kmfciofb ` unf hibuof stqu`n pr``ohamkfs hin gibfs kf n`snf hir9
. Hiosmk`r`,
\
y
tikis is oün`ris k` s`ms fbcfrmsnis qu` s` pik`n igt`r fbt`rfoki f irk`n kis fbcfrmsnis ki oün`ri 646355.
Vufotis k`ss`s oün`ris sèi pfr`s ` n`oir`s ki qu` 755555 9 (F) 67
(G) 7;
(H) 84
(K) ;1
•
= 6 5 7
©
8
Urigfgmbmkfk`s ` Hingmoftørmf • Nft`nætmhf F ‘ 67¼ foi
. K`
un crupi k` k`z fnmcis, s`ms rfpfz`s ` quftri rfpfrmcfs, vèi s`r `shibamkis, fi fhfsi, quftri fnmcis pfrf dirnfr unf hinmssèi. @ssf hinmssèi t`ræ k` t`r nfms rfpfz`s qu` rfpfrmcfs. Xfg`-s` qu` i [inæs ` i Tfshi dfrèi pfrt` kf hinmssèi. Vufotfss hinmssð`s Vufotf hinmssð`s kmd`r`ot`s kmd`r`ot`s pik`rèi s`r dirnfkfs o`stfs hiokmãð`s9 hiokmãð`s9 (F) 77
. Of
(G) 71
(H) 85
(K) =0
Dmcurf fi bfki `stæ r`pr`s`otfki un tfgub`mri hin vmot` ` hmohi hfsfs. 0
; \ \\\\ 8 \ \ Fs p`ãfs pr`tfs sèi oun`rfkfs k` 6 f 67 , ` fs p`ãfs grfohfs oèi tìn qufbqu`r ou- \ n`rfãèi. 7 \ \ @shr`vf unf `xpr`ssèi qu` p`rnmt` k`t`rnmofr i oün`ri k` nfo`mrfs `n qu` s` pi6 \ \ k`n kmspir p`ãfs, k` dirnf qu` fs p`ãfs pr`tfs ihup`n unf bmoaf mot`mrf ` i prikuti \ Ur`t`ok`-s` hibihfr o`st` tfgub`mri s`ms p`ãfs grfohfs ` kiz` p`ãfs pr`tfs k` dirnf f qu` hfkf p`ãf ihup` unf ` unf sø hfsf.
f
kis oün`ris k`ssf bmoaf s`lf pfr. Hiosmk`r` . Hiosmk`r`
g
h
k
`
tikis is oün`ris oün`ris ofturfms ofturfms k` hmohi fbcfrmsnis fbcfrmsnis `otr` 85 55 555 5 ` 05 55 555 5.
K`st`s oün`ris, qufotis tìn `xftfn`ot` kims fbcfrmsnis ; 9 (F) ;14
Hiosmk`r` . Hiosmk`r`
(G) =37
(H) 7=64
(K) 8;57
tikis is oün`ris oün`ris ofturfms ofturfms k` hmohi fbcfrmsnis. fbcfrmsnis.
K`st`s oün`ris, qufotis tìn `xftfn`ot` `xftfn`ot` trìs fbcfrmnis fbcfrmnis 5 9 (F) 16
(G) 87;
(H) 165
(K) 6=;;
. K`
un crupi k` k`z liv`os, hmohi rfpfz`s ` hmohi rfpfrmcfs, vèi s`r `shibamkis, fi fhfsi, quftri fbuois pfrf dirnfr unf hinmssèi. F hinmssèi t`ræ k` s`r hiostmtuîkf pir, p`bi n`ois, un rfpfz ` unf rfpfrmcf. I [inæs ` i Dmbmp` sèi kims fbuois k`ssf turnf qu` dfrèi pfrt` kf hinmssèi. Vufotfss hinmssð`s Vufotf hinmssð`s kmd`r`ot`s kmd`r`ot`s s` pik`n dirnfr dirnfr o`stfs hiokmãð`s9 hiokmãð`s9 (F) 70
. I
(G) 45
(H) 605
(K) 755
høkmci k` fh`ssi f unf hiotf k` `-nfmb í hiostmtuîki pir trìs vicfms ` kims fbcfrmsnis înpfr`s.
Vufotis høkmcis kmd`r`ot`s `xmst`n hin trìs vicfms mcufms9 (F) 755
(G) 705
(H) 6555
(K) 6705
. I
Gruoi ` i Wum sèi kims kis k`z fbuois qu` igtmv`rfn oitf sup`rmir f 63 vfbir`s ounf kfkf kmshmpbmof ` qu` dirfn sugn`tmkis å k`d`sf k`ssf oitf ounf privf irfb. I Urid`ssir k`ssf kmshmpbmof kmvmkmu is k`z fbuois fb`ftirmfn`ot` pir kims kmfs, s`oki qu` hfkf kmf í ihupfki, oi næxmni, p`bf k`d`sf k` oitf k` s`ms fbuois.
K` qufotfs dirnfs pik`n is k`z fbuois s`r kmstrmguîkis p`bis kims kmfs, k` dirnf f qu` i Gruoi ` i Wum k`d`okfn f suf oitf oi n`sni kmf9
i r m ` r r ` u C b ` u c m N i o u O •
n i h . t f n s m f n b f o m s •
= 6 5 7
;
©
Urigfgmbmkfk`s ` Hingmoftørmf • Nft`nætmhf F ‘ 67¼ foi
. Hiosmk`r`
tikis is oün`ris qu` s` igt`n igt`r fbt`rfoki f irk`n kis fbcfrmsnis 5 5 6 6 7 0
Vufotis oün`ris k` 4 fbcfrmsnis sèi pfr`s ` nfmir`s qu` 7555559 (F) 61
(G) 7;
(H) 85
(K) 0;
. Hiosmk`r`
is oün`ris hiostmtuîkis pir hmohi fbcfrmsnis k` 5 f = tfms qu` tìn `xftfn`ot` trìs fbcfrmsnis 3 ` sè sèii nfmir`s qu` 45 555. 555. Vufotiss oün`ris Vufoti oün`ris `xmst`n `xmst`n o`stfs hiokmãð`s9
(F) 84 (F) 84
(G) 651 (G) 651
(H) 0;5 (H) 0;5
(K) 0=; (K) 0=;
. Pn
sfhi hiotín oiv` gibfs hibirmkfs oun`rfkfs k` 6 f = , mokmstmocuîv`ms fi tfti, tfms qu` fs gibfs oun`rfkfs k` 6 f 8 sèi fnfr`bfs, fs gibfs oun`rfkfs k` ; f 4 sèi v`rn`bafs, ` fs gibfs oun`rfkfs k` 3 f = sèi fzums. Hiosmk`r` qu` sèi s`b`hmiofkfs 1 kfs = gibfs ` `stfs sèi kmspistfs bfki f bfki. K` qufotfs nfo`mrfs s` pik`n kmspûr fs gibfs, k` niki qu` fs gibfs hin f n`snf hir stqu`n luotfs9
. Pn
crupi k` = p`ssifs vfm k` dírmfs pfrf i Fbcfrv`, b`vfoki kims hfrris k` 0 bucfr`s hfkf. Xfg`-s` qu` qufbqu`r unf kfs p`ssifs hios`cu` hiokuzmr. K` qufotfs dirnfs s` pik`n kmstrmgumr is fnmcis p`bis kims hfrris9 (F) 65 H 0
. Hiosmk`r`
(G) = H ;
Ó
=
H 0
(H) = H ;
(K) = F;
Ó
=
F0
un bit` k` ;5 fnistrfs k` æcuf kmstmocuîv`ms qu` vèi s`r t`stfkfs p`bi quînmhi.
Xfg`-s` qu` f prigfgmbmkfk` k` unf fnistrf k` æcuf `stfr hiotfnmofkf pir sugstçohmfs quînmhfs í 0% . I quînmhi fpøs dfz`r is t`st`s, hibihf fs fnistrfs hiotfnmofkfs bfki f bfki oun kis `xtr`nis ki bit`. Mokmqu` f `xpr`ssèi qu` p`rnmt` hfbhubfr i oün`ri k` nfo`mrfs qu` i quînmhi kmspir fs ;5 fnistrfs oi bit`. . Hiosmk`r`
unf turnf k` 75 fbuois, `n qu` `xmst`n 65 rfpfrmcfs, `otr` fs qufms `stèi f Lifof ` f Moìs, ` 65 rfpfz`s.
Pnf kfs sfbfs iok` f turnf t`n fubfs t`n 0 stbfs hin 0 n`sfs mokmvmkufms hfkf. Xfg`-s` qu`<
i r m ` r r ` u C b ` u c m N i o u O •
n i h . t f n s m f n b f o m s
• f
prmn`mrf stbf k`v` s`r ihupfkf fp`ofs pir rfpfrmcfs:
• f
s`cuokf stbf k`v` s`r ihupfkf fp`ofs pir rfpfz`s:
• f
übtmnf stbf t`n fp`ofs unf p`ssif qu` í un rfpfz.
K` qufotfs dirnfs kmd`r`ot`s pik`n is fbuois kf turnf s` kmspir o`stf sfbf9 . I
oün`ri ki hfrtèi k` hmkfkèi pirtucuìs í hiostmtuîki pir 1 fbcfrmsnis k` 5 f = .
Vufotis oün`ris k` hfrtèi k` hmkfkèi tìn `xftfn`ot` un = oi übtmni kîcmti, ` tìn `xftfn`ot` kims ; ` kims 8 , s`oki is r`stfot`s fbcfrmsnis kmd`r`ot`s9 (F) 3805 (F) 3805
(G) 66345 (G) 66345
(H) ;;655 (H) ;;655
(K) 35045 (K) 35045
•
= 6 5 7
©
0
Urigfgmbmkfk`s ` Hingmoftørmf • Nft`nætmhf F ‘ 67¼ foi
. Hiosmk`r`
tikis is oün`ris qu` s` pik`n igt`r fbt`rfoki f irk`n kis fbcfrmsnis ki oün`ri 67 80 801 1.
Vufotis k`ss`s oün`ris sèi pfr`s ` n`oir`s ki qu` 75 55 555 59 67 (F) 67 (F)
. X`ms
(G) 61 (G) 61
(H) 7; (H) 7;
(K) 85 (K) 85
liv`os, trìs rfpfrmcfs ` trìs rfpfz`s, vèi kmspûr-s`, bfki f bfki, pfrf unf diticrfstf.
K` qufotfs nfo`mrfs i pik`n dfz`r, k` niki qu` fs rfpfrmcfs ` is rfpfz`s stqu`n kmspistis fbt`rofkfn`ot`9 (F) 84 (F) 84
(G) ;1 (G) ;1
(H) 4; (H) 4;
(K) 37 (K) 37
. F
pfsswirk pfrf fh`k`r f unf kfkf pbftfdirnf of Mot`ro`t t`n hinprmn`oti k` 3 hfrfht`r`s s`oki qu` í igrmcftørmi `xmstmr fbcfrmsnis ` b`trfs ki fbdfg`ti pirtucuìs of n`snf. Vufotfs sèi fs pfsswirks qu` hiotín `xfhtfn`ot` trìs "f" ` un ` un sø fbcfrmsni9 (F) 3 H 8
(H) 3
;
8
(G) 3 H 8
Ó H Ó 65 Ó 77 F Ó ; Ó 65 Ó 77 6
8
(K) 3
8
;
8
Ó H Ó = Ó 78 F Ó 65 Ó 78 6
8
8
i r m ` r r ` u C b ` u c m N i o u O •
n i h . t f n s m f n b f o m s •
= 6 5 7
4
©
Urigfgmbmkfk`s ` Hingmoftørmf • Nft`nætmhf F ‘ 67¼ foi
7 [rmçocubi k` Ufshf Ufshfb. b. Uriprm`kfk` Uriprm`kfk`ss kfs Hingmofãð`s . X`lfn f ` g kufs
hiostfot`s r`fms.
Hiosmk`r`, pfrf un kfki o ∁ O pfr, f bmoaf o ki [rmçocubi k` Ufshfb tfb qu`< • i
nfmir `b`n`oti k`ssf bmoaf t`n vfbir f :
• i
nfmir `b`n`oti kf bmoaf pfr s`cumot` t`n vfbir g
Vufb i vfbir ki s`cuoki nfmir `b`n`oti kf bmoaf o 9 (F)
g
7
(G)
g
7
+ f
(H)
f
7
(K)
g
7
∗ f
i . X`lf g i
vfbir ki s`xti `b`n`oti k` unf bmoaf ki [rmçocubi k` Ufshfb, tfb qu` i vfbir ki s`u kíhmni imtfvi `b`n`oti tfngín í mcufb f g .
X`b`hmiof-s`, fi fhfsi, un `b`n`oti kf bmoaf s`cumot` ki [rmçocubi k` Ufshfb. Vufb í f prigfgmbmkfk` ki `b`n`oti `shibamki t`r vfbir nfmir qu` g 9 9 (F)
66 78
. Hiosmk`r`
(G)
68 78
(H)
0 67
(K)
3 67
f bmoaf ki [rmçocubi k` Ufshfb tfb qu` i vfbir ki s`u qumoti `b`n`oti í mcufb fi ki vmcísmni `b`n`oti.
Vufb í i nfmir `b`n`oti kf bmoaf s`cumot` 9 (F) 6807531
. Hiosmk`r`
(G) 735;604
(H) 0 75 755 5 85 855 5
(K) =403355
f bmoaf o ki [rmçocubi k` Ufshfb tfb qu` f sinf kis übtmnis quftri `b`n`otis í =8 .
Xfg`-s` fmokf qu` i qufrti `b`n`oti kf bmoaf o + 6 í mcufb f 1; . Vufotis `b`n`otis t`n f bmoaf o 9 (F) 3
(G) 1
. Hiosmk`r` f bmoaf ki
(H) =
(K) 65
[rmçocubi [rmçocubi k` Ufshfb tfb qu` i s`u kíhmni s`cuoki `b`n`oti t`n vfbir nfmir qu` is k`nfms `b`n`otis
kf bmoaf. i r m ` r r ` u C b ` u c m N i o u O •
n i h . t f n s m f n b f o m s
Vufb f irk`n ki `b`n`oti kf bmoaf s`cumot` huli vfbir í mcufb fi ki imtfvi `b`n`oti k`ssf n`snf bmoaf9 (F) 60
Hiosmk`r` . Hiosmk`r`
(G) 64
(H) 63
(K) 61
f bmoaf ki [rmçocubi [rmçocubi k` Ufshfb tfb qu` i oioi `b`n`oti t`n mcufb vfbir fi kíhmni qufrti qufrti `b`n`oti.
Vufb í f sinf k` tikis is `b`n`otis kf bmoaf fot`rmir 9 (F) 7476;;
(G) 07; 07; 711
(H) 6 5; 5;1 1 03 034 4
(K) 7 5= 5=3 3 60 607 7
•
= 6 5 7
©
3
Urigfgmbmkfk`s ` Hingmoftørmf • Nft`nætmhf F ‘ 67¼ foi
Hiosmk`r` . Hiosmk`r`
f `xp`rmìohmf `xp`rmìohmf fb`ftørmf fb`ftørmf qu` hiosmst` `n `shiba `shiba`r `r kims `b`n`otis fi fhfsi kf bmoaf 68 ki [rmçocubi k` Ufshfb.
Vufb í f prigfgmbmkfk` ki prikuti k`ss`s `b`n`otis s`r sup`rmir f 68 9 (F)
. F
67 68
(G)
38 31
(H)
10 =6
(K)
14 =6
sinf kis hmohi übtmnis `b`n`otis k` unf h`rtf bmoaf ki [rmçocubi k` Ufshfb í 704 .
Vufb i vfbir kf sinf kis t`rh`mri ` qumoti `b`n`otis kf bmoaf s`cumot`9 (F) =8
. Ufrf
(G) 685
(H) 700
un kfki vfbir k` o ∁ O sfg`-s` qu`
o+6
(K) 830
o +8
H 7 > f `
H 8 > g
Vufb í i vfbir kf sinf kis übtmnis quftri `b`n`otis kf bmoaf o ki [rmçocubi k` Ufshfb9 (F) g
∗f
. Hiosmk`r`
(G) g
∗ 7f
(H) g
∗ 8f
(K) 7 (K) 7 g
∗ 0f
f bmoaf ki trmçocubi k` Ufshfb tfb qu` i s`u imtfvi `b`n`oti í mcufb fi s`u kíhmni s`cuoki `b`n`oti.
Vufb i nfmir `b`n`oti kf bmoaf s`cumot`9 (F) ;8 (F) ;8 30 301 1
. Hiosmk`r`
(G) ;1 (G) ;1 47 475 5
(H) 30 (H) 30 01 017 7
(K) =7 (K) =7 83 831 1
f bmoaf o ki trmçocubi k` Ufshfb `n qu` f kmd`r`oãf `otr` i t`rh`mri ` p`oübtmni `b`n`oti í 73 .
Vufb f sinf k` tikis is `b`n`otis kf bmoaf s`cumot`9 (F) 704 (F) 704
. Hiosmk`r`
(G) 067 (G) 067
(H) 657; (H) 657;
(K) 75;1 (K) 75;1
f bmoaf ki trmçocubi k` Ufshfb `n qu` i qumoti `b`n`oti í mcufb fi kíhmni `b`n`oti.
Vufb í i vfbir kf sinf kis quftri n`oir`s `b`n`otis kf bmoaf s`cumot`9 (F) 71
(G) 85
(H) 87
(K) 8;
8 Gmoøn Gmoønmi mi k` O`wt O`wtio io . I
8
k`s`ovibvmn`oti k` x
8
∗ x
66
t`n un t`rni k` prmn`mri crfu.
Vufb í i hi`sthm`ot` k`ss` t`rni9 (F)
. Pn
∗667 744
(G) 4;=08=
kis t`rnis ki k`s`ovibvmn`oti k`
Vufb í `ss` t`rni9 (F) 1
∗6715
(G) 6
;
(H)
∗376365
(K) 6517040
•
4
x 7
∗ , hin x
i r m ` r r ` u C b ` u c m N i o u O
x > 5, oèi k`p`ok` kf vfrmæv`b x .
(H) 7;5
(K) 81;5
n i h . t f n s m f n b f o m s •
= 6 5 7
©
Urigfgmbmkfk`s ` Hingmoftørmf • Nft`nætmhf F ‘ 67¼ foi
. Hiosmk`r`
7
i k`s`ovibvmn`oti k` x +
6 x 4
o
, hin x ? 5 , ` o ∁ O.
Nistr` qu` s` `xmst` un t`rni mok`p`ok`ot` oi k`s`ovibvmn`oti, `otèi o í nübtmpbi k` ; .
. Ufrf
∜
un h`rti vfbir k` f ∁ W+ , un kis t`rnis k` k`s`ovibvmn`oti k` ( x y + + f7 )65 í 66075x y 7 .
Vufb í `ss` vfbir k` f 9 (F) 6 (F) 6
(G)
∜ 7
(H) 7 (H) 7
(K) ; (K) ;
i r m ` r r ` u C b ` u c m N i o u O •
n i h . t f n s m f n b f o m s •
= 6 5 7
©
=
Urigfgmbmkfk`s ` Hingmoftørmf • Nft`nætmhf F ‘ 67¼ foi
; Hæbh Hæbhubi ubi k` Uri Urigfgmb gfgmbmkfk` mkfk`s. s. W`cr W`crf f k` Bfpb Bfpbfh` fh` . Pnf
r`vmstf k` nüsmhf grmtçomhf t`v` f momhmftmvf k` hrmfr un moquírmti ofhmiofb k` dirnf f sfg`r qufb í f ipmomèi kis afgmtfot`s oi W`moi Pomki r`bftmvfn`ot` f qufb hiosmk`rfn s`r f n`bair gfokf grmtçomhf k` tikis is t`npis. Fbcuos kis moqumrmkis qu` s`b`hmiofrfn f gfokf [a` G`ftb`s hini n`bair gfokf mocb`sf k` tikis is t`npis dirfn fmokf s`b`hmiofkis s`b`hmiofkis pfrf un s`cuoki moquírmti, moquírmti, `n qu` dim p`kmki qu` s`b`hmiofss`n s`b`hmiofss`n fqu`b` qu` hiosmk`rfn hiosmk`rfn s`r i n`bair æbgun kf gfokf. Xfg`-s` qu` trìs `n hfkf k`z k`ss`s moqumrmkis s`b`hmiofrfn i æbgun Fgg`y Wifk hini i s`u dfvirmti. @shiba`rfn-s`, @shiba` rfn-s`, fi fhfsi, kims moqumrmkis moqumrmkis o`st` s`cuoki s`cuoki moquírmti. moquírmti. Xfg`-s` qu` f prigfgmbmkfk` k`, p`bi n`ois, un k`b`s oèi t`r hiosmk`rfki i æbgun Fgg`y Wifk hini i n`bair kf gfokf í
86 . 8;
K`t`rnmo` i oün`ri k` p`ssifs qu` dirfn qu`stmiofkfs oi s`cuoki moquírmti.
. Oun
`shrmtørmi `n Bmsgif k` unf `npr`sf t`hoibøcmhf trfgfbafn 70 p`ssifs< 61 rfpfz`s ` 3 rfpfrmcfs.
Tfm s`r dirnfkf unf hinmssèi ircfomzfki ircfomzfkirf rf k` un lfotfr k` Oftfb qu` s`ræ hiostmtuîkf hiostmtuîkf pir 4 p`ssifs. p`ssifs. Xfg`-s` fmokf qu` f hinmssèi ircfomzfkirf t`ræ k` s`r nmstf. I Nmcu`b ` i [ainfs sèi kims kis `npr`cfkis o`ss` `shrmtørmi. Tfm s`r `shibamkf, fi fhfsi, unf hinmssèi `otr` fs hinmssð`s pissîv`ms. Vufb í f prigfgmbmkfk` kf hinmssèi t`r p`bi n`ois quftri rfpfz`s ` i Nmcu`b ` i [ainfs p`rt`oh`r`n smnubtfo`fn`ot` f `ssf n`snf9 Fpr`s`ot` i r`subtfki of dirnf k` kîzmnf, hin frr`kiokfn`oti ås h`otísmnfs.
. Hiosmk`r`
unf turnf k` kíhmni s`cuoki foi hiostmtuîkf pir 6; rfpfz`s ` 65 rfpfrmcfs.
Tfm s`r dirnfkf unf hinmssèi hin 8 rfpfz`s ` 8 rfpfrmcfs kf turnf. I Nmcu`b ` i Dmbmp` sèi kims fbuois k`ssf turnf, ` f B`ioir í f k`b`cfkf k` turnf. Tfm s`r `shibamkf, fi fhfsi, unf hinmssèi `otr` tikfs fs hinmssð`s pissîv`ms. Vufb í f prigfgmbmkfk` kf k`b`cfkf p`rt`oh`r å hinmssèi `shibamkf, ` i Dmbmp` ` i Nmcu`b oèi p`rt`oh`r`n smnubtfo`fn`ot` f `ssf n`snf9 Fpr`s`ot` i r`subtfki of dirnf k` kîzmnf, hin frr`kiokfn`oti ås h`otísmnfs.
. Of
Dmcurf fgfmxi `stæ r`pr`s`otfkf unf hmrhuod`rìohmf ` is piotis F , G , H , K , @ , D , C , A , M . Tèi s`r `shibamkis kims piotis p`rt`oh`ot`s fi kmçn`tri D ZF@ ^ ` un pioti p`rt`oh`ot` å hmrhuod`rìohmf (`xhbumoki is piotis F ` @ ). Vufb f prigfgmbmkfk` kis trìs piotis `shibamkis k`stomr`n un trmçocubi r`tçocubi9 (F)
6
65 8 (H) 65
F
G
H
C
K
•
6
(G)
0 7 (K) 0
@
i r m ` r r ` u C b ` u c m N i o u O n i h . t
A
M
f n s m f n b f o m s •
= 6 5 7
65
©
Urigfgmbmkfk`s ` Hingmoftørmf • Nft`nætmhf F ‘ 67¼ foi
. I
U`kri ` i Cum r`cmstfrfn is r`subtfkis kis 70 licis k` dut`gib qu` kmsputfrfn oi stn-k`-s`nfof of UX; .
Xfg`-s` qu`, o`ss` stn-k`-s`nfof, i U`kri v`oh`u 60 licis ` i Cum v`oh`u is r`stfot`s. I U`kri U`kri ` i Cum, of s`cuokf-d`mrf s`cuokf-d`mrf s`cumo s`cumot`, t`, kmsputfrfn kmsputfrfn nfms o (o ≠ 4) licis, s`oki qu` i U`kri v`oh`u 4 k`ss`s licis. Hiosmk`r` fcirf qu` vèi s`r `shibamkis kims licis fi fhfsi `otr` is kmsputfkis oi stn-k`-s`nfof ` of s`cuokf-d`mrf. Xfg`-s` qu` f prigfgmbmkfk` k` s`r`n `shibamkis kims licis `n qu` i U`kri v`oh`u í
4 . 63
K`t`rnmo` qufotis licis í qu` i U`kri ` i Cum kmsputfrfn of s`cuokf-d`mrf. . Of
Dmcurf fgfmxi, `stæ r`pr`s`otfki, oun r`d`r`ohmfb i.o x Iy , i ihtøcioi r`cubfr Z FGHK@DCA ^ h`otrfki of irmc`n ki r`d`r`ohmfb ` unf hmrhuod`rìohmf. H
Hiosmk`r` f `xp`rmìohmf fb`ftørmf qu` hiosmst` `n `shiba`r, fi fhfsi, trìs vírtmh`s ki ihtøcioi Z FGHK@DCA ^.
G K
Vufb f prigfgmbmkfk` ki trmçocubi qu` uo` is trìs vírtmh`s `shibamkis t`r un bfki qu` hiostmtum un kmçn`tri kf hmrhuod`rìohmf9 (F)
7 3
(G)
8 3
(H)
; 3
(K)
y
F @
x
I
0 3
A D C
. Hiosmk`r`,
oun r`d`r`ohmfb i.o Ixyz , i prmsnf r`ti Z IFGHK@DC ^ r`pr`s`otfki of Dmcurf fi bfki.
z
Xfg`-s` qu`< • fs
C
gfs`s ki prmsnf sèi qufkrfkis pfrfb`bis fi pbfoi x Iy :
• is
piotis A ` M sèi is piotis níkmis kfs kmfciofms kfs dfh`s ZFG@D ^ ` Z CD@ K^, r`sp`tmvfn`ot`.
Tèi s`r `shibamkis, fb`ftirmfn`ot`, trìs piotis `otr` is vírtmh`s ki prmsnf ` is piotis A ` M .
K
M
D
@ I A x
H
y
F
@shr`vf f `xpr`ssèi qu` p`rnmt` hfbhubfr f prigfgmbmkfk` kis trìs piotis
G
Iz z . `shibamkis `shibam kis k`stomr`n un pbfoi p`rp`okmhubfr p`rp`okmhubfr fi `mxi I
. @n
oiv`ngri k` 7561 k`hirr`ræ, `n K`bdt, un `ohiotri mot`rofhmiofb k` `sp`hmfbmstfs ki s`tir f`ri`spfhmfb, iok` pfrtmhmpfrèi 45 hm`otmstfs. Kis `sp`hmfbmstfs pr`s`ot`s oi hiocr`ssi sfg`-s` qu` trìs `n hfkf hmohi sèi aibfok`s`s. Ur`t`ok`-s` Ur`t`o k`-s` `shiba`r, fi fhfsi, imti hm`otmstfs hm`otmstfs pfrf un lfotfr lfotfr k` hiodrft`romz hiodrft`romzfãèi. fãèi.
i r m ` r r ` u C b ` u c m N i o u O •
n i h . t f n s m f n b f o m s •
= 6 5 7
©
K`t`rnmo` K`t`rnm o` f prigfgmbmk prigfgmbmkfk` fk` k` s`r`n `shibamkis, `shibamkis, p`bi n`ois, kims `sp`hmfbmstfs `sp`hmfbmstfs aibfok`s`s. aibfok`s`s. Fpr`s`ot` i r`subtfki hin frr`kiokfn`oti ås h`otísmnfs.
. Hiosmk`r`
f bmoaf o + 6 ki [rmçocubi k` Ufshfb tfb qu` f sinf ki p`oübtmni ` übtmni `b`n`otis í 67 .
@shiba`n-s` kims `b`n`otis fi fhfsi kf bmoaf o iu kf bmoaf o + 6 ki [rmçocubi k` Ufshfb. K`t`rnmo` K`t`rnm o` f prigfgmbmk prigfgmbmkfk` fk` k` kims `b`n`otis `shibamkis `shibamkis s`r`n mcufms. Fpr`s`ot` i r`subtfki hin frr`kiokfn`oti ås h`otísmnfs. 66
Urigfgmbmkfk`s ` Hingmoftørmf • Nft`nætmhf F ‘ 67¼ foi
. I
[inæs d`z unf foæbms` fi hirr`mi qu` t`n ha`cfki fi s`u nfmb, ` hiostftiu qu` 65% kis `nfmbs qu` r`h`g` sèi kmr`hmiofkis pfrf f hfmxf k` spfn. Ufrf Ufrf fbín kmssi kmssi oitiu oitiu qu` kfs n`osfc`os n`osfc`os qu` sèi kmr kmr`hmi `hmiofkf ofkfss pfrf pfrf f hfmxf hfmxf k` spfn, 45% tìn vîrus. Hiosmk`r` qu` ounf kfkf s`nfof, i [inæs tmoaf 75 nfmbs of hfmxf k` spfn. @shiba`n-s`, fi fhfsi, imti k`ss`s nfmbs kf hfmxf k` spfn. 75
F prigfgmbmkfk` k`, `otr` `ss`s nfmbs, afv`r p`bi n`ois un qu` t`oaf vîrus í
H 1 6 . 75 H 1
∗
@bfgir` @bfgi r` unf hinpismãèi of qufb `xpbmqu` f `xpr`ssèi `xpr`ssèi fpr`s`otfkf. fpr`s`otfkf. Of suf hinpismãèi, `ouohm` f r`crf k` Bfpbfh`, `xpbmqu` i oün`ri k` hfsis pissîv`ms ` i oün`ri k` hfsis dfviræv`ms. . Hiosmk`r`
unf turnf k` 75 fbuois, `n qu` `xmst`n 65 rfpfrmcfs, `otr` fs qufms `stèi f Lifof ` f Moìs, ` 65 rfpfz`s.
Tfm s`r dirnfkf unf hinmssèi k` 0 fbuois, `n qu` i oün`ri k` rfpfrmcfs k`v` s`r sup`rmir fi oün`ri k` rfpfz`s. @shr`vf f `xpr`ssèi `xpr`ssèi qu` p`rnmt` p`rnmt` hfbhubfr hfbhubfr f prigfgmbmk prigfgmbmkfk` fk` k`, `shiba`oki `shiba`oki fb`ftirmfn`ot` fb`ftirmfn`ot` unf hinmssèi, hinmssèi, `stf s`r hiostmhiostmtuîkf p`bf Lifof ` f Moìs smnubtfo`fn`ot`.
. Pnf
hfmxf hiotín s`ms gibfs oun`rfkfs k` 5 f 0, mokmstmocuîv`ms fi tfti.
W`tmrfn-s`, suh`ssmvfn`ot`, fi fhfsi ` s`n r`pismãèi, kufs gibfs kf hfmxf, r`cmstfoki f sinf kis oün`ris kfs gibfs sfîkfs. Vufb f prigfgmbmkfk` k` oèi sfmr f gibf 7, qufoki f sinf kis oün`ris kfs gibfs sfîkfs í înpfr9 Fpr`s`ot` i r`subtfki of dirnf k` drfhãèi mrr`kutîv`b.
. Ki
pbfot`b momhmfb k` unf `qumpf k` dut`gib pirtucu`sf pirtucu`sf hin 75 licfkir`s, licfkir`s, sfg`-s` qu` 7 `n hfkf 0 licfkir`s licfkir`s kf `qumpf tìn ofhmiofbmkfk` pirtucu`sf. Luotfrfn-s` å `qumpf o licfkir`s s`n ofhmiofbmkfk` pirtucu`sf. @shiba`n-s`, fi fhfsi ` suh`ssmvfn`ot`, kims licfkir`s kf `qumpf k` dut`gib. Xfg`-s` qu` f prig prigfgmbmk fgmbmkfk` fk` kis kims licfkir`s licfkir`s t`r`n ofhmiofbmkfk` ofhmiofbmkfk` pirtucu`sf pirtucu`sf í
; . 88
K`t`rnmo` o . . I
U`kri ` i Dmbmp` vèi vmflfr kurfot` fbcuos kmfs f Fn`st`rkèi.
Kurfot` un pfss`mi p`bf hmkfk`, i U`kri ` i Dmbmp` qums`rfn `stfhmiofr fs sufs gmhmhb`tfs, kmstmocuîv`ms p`bf hir, pfrf vmsmtfrr un nus`u. vmsmtf I `stfhmiofn`oti tmoaf unf bitfãèi k` 75 gmhmhb`tfs, s`oki hiostmtuîki pir 7 stbfs iok` s` pik`rmf `stfhmiofr, pfrf hfkf unf kfs stbfs, 65 gmhmhb`tfs bfki f bfki. O`ss` kmf, f stbf kf dr`ot` `stfvf s`n qufbqu`r gmhmhb`tf `stfhmiofkf, ` f stbf k` træs fp`ofs tmoaf ; bucfr`s vfcis hirr`spiok`ot`s f 7 gmhmhb`tfs `n hfkf un kis `xtr`nis.
i r m ` r r ` u C b ` u c m N i o u O •
Vufb f prigfgmbmkfk` k`, `stfhmiofoki fs gmhmhb`tfs `n kims bucfr`s vfcis fi fhfsi, fs gmhmhb`tfs ki U`kri ` ki Dmbmp`
n i h . t
sthfr`n bfki f bfki9 Fpr`s`ot` i r`subtfki hin frr`okiokfn`oti ås h`otísmnfs.
f n s m f n b f o m s •
= 6 5 7
67
©
Urigfgmbmkfk`s ` Hingmoftørmf • Nft`nætmhf F ‘ 67¼ foi
. Hiosmk`r`
fcirf un sfhi hiostmtuîki pir imti gibfs oun`rfkfs k` 6 f 1 < kufs gibfs fzums, kufs gibfs v`rk`s, kufs gibfs bfrfolfs ` kufs gibfs pr`tfs. Fs imti gibfs ki sfhi s`rèi kmspistfs, fi fhfsi, bfki-f-bfki. Vufb f prigfgmbmkfk` kfs gibfs kf n`snf hir sthfr`n luotfs9 Fpr`s`ot` i r`subtfki of dirnf k` drfãèi mrr`kutîv`b.
.
Vuftri hfsfms hinprfrfn hinprfrfn gmba`t`s gmba`t`s pfrf un hioh`rti, hioh`rti, s`oki i Cumba`rn` Cumba`rn` unf k`ssfs p`ssifs. Dirfn s`b`hhmiofkfs 675 p`ssifs, `otr` fs qufms `stèi i Cumba`rn` ` f suf ofnirfkf, pfrf un sirt`mi pfrf mr fis gfstmkir`s ` hioa`h`r is frtmstfs, hiotuki sø ; p`ssifs t`rèi `ssf ipirtuomkfk`. Vufb f prigfgmbmkfk` k` i Cumba`rn` ` f suf ofnirfkf oèi `stfr`n smnubtfo`fn`ot` `otr` is `shibamkis pfrf mr hioa`h`r f gfokf9 Fpr`s`ot` i vfbir p`kmki of dirnf k` drfhãèi mrr`kutîv`b.
. Oi
r`d`r`ohmfb i.o x Iy kf stcurf, `stæ r`pr`s`otf r`pr`s`otfki ki un ihtøcioi ihtøcioi r`cubfr Z FGHK@DCA ^ moshrmti ounf hmrhuod`rìohmf. y H G K F x @ A D C
K`t`rnmo` f prigfgmbmkfk` k`, `shiba`oki kims vírtmh`s fi fhfsi, `st`s k`stomr`n unf r`tf k` k`hbmv` o`cftmvi. Fpr`s`ot` i r`subtfki `n dirnf k` drfãèi mrr`kutîv`b. . Fi
i r m ` r r ` u C b ` u c m N i o u O
fgrmci k` un pricrfnf k` mot`rhçngmi, dirfn s`b`hhmiofkis 85 fbuois k` `otr` is `stukfot`s kf Dfhubkfk` k` @oc`oafrmf kf Pomv`rsmkfk` ki Uirti ` i Mostmtuti Xup`rmir [íhomhi pfrf r`fbmzfr unf vmsmtf f Afngurci. Fp`ofs kims hursis `stfrèi r`pr`s`otfkis of vmfc`n ` sèi `st`s @oc`oafrmf N`hçomhf ` @oc`oafrmf @b`htritíhomhf ` k` Hinputfkir`s. K` tikis is `stukfot`s sfg`-s` qu`< • 61
fbuois `stukfn @oc`oafrmf N`hçomhf, s`oki 1 k`st`s kf Dfhubkfk` k` @oc`oafrmf kf Pomv`rsmkfk` ki Uirti: • Is r`stfot`s ; fbuois qu` dr`qu`otfn f Dfhubkfk` k` @oc`oafrmf kf Pomv`rsmkfk` ki Uirti `stukfn @oc`oafrmf @b`htritíhomhf ` k` Hinputfkir`s. K`z fnmcis ki n`sni hursi vèi vmsmtfr i Uirti k` Afngurci.
•
n i h . t f n s m f n b f o m s
F prigfgmbmkfk` k` tikis is fnmcis s`r`n kf n`snf dfhubkfk` í<
6
61
@bfgir` @bfgi r` unf hinpismãèi of qufb `xpbmqu` f `xpr`ssèi `xpr`ssèi fpr`s`otfkf. fpr`s`otfkf.
.
67 65
H +
65
H
Of suf r`spistf, `ouohm` f W`crf k` Bfpbfh`, ` `xpbmqu` i oün`ri k` hfsis pissîv`ms ` i oün`ri k` hfsis dfviræv`ms.
•
= 6 5 7
©
68
Urigfgmbmkfk`s ` Hingmoftørmf • Nft`nætmhf F ‘ 67¼ foi
0 K`stomãèi fx fxminætmhf minætmhf k` prigfgmbmkfk`. Uriprm`kfk`s kfs prigfgmbmkfk`s . X`lf @ un
hioluoti stomti, U unf prigfgmbmkfk` `n U (@ ) ` F, G ∁ U (@ ).
Xfg`-s` qu`< • F ` G sèi • U (F) >
fhiot`hmn`otis `qumprivæv`ms
5,4
Vufb kis s`cumot`s vfbir`s oèi pik` s`r i vfbir k` U (F ∬ G ) 9 (F) 5,8
. X`lf @ un
(G) 5,;
(H) 5,0
(K) 5,4
hioluoti stomti, U unf prigfgmbmkfk` `n U (@ ) ` F, G ∁ U (@ ).
Xfg`oki qu` G `stæ hiotmki `n F , qufb í i vfbir k` U (F ∭ G )9 (F) U (F
∭ G)
. X`lf @ un
(G) 5 (G) 5
(H) U (F)
(K) U (F
∭ G)
hioluoti stomti, U unf prigfgmbmkfk` `n U (@ ) ` F, G ∁ U (@ ).
Xfg`-s` qu`< • U (F • U (F
∭ G) > 8U (F ∭ G) G ) > U (F
∭
G)
∭
Nistr` qu` U (F ∬ G ) > U (F ∬ G ).
4 Urigfgmbmkfk` Hiokmhmiofkf . Pnf
r`vmstf k` nüsmhf grmtçomhf t`v` f momhmftmvf k` hrmfr un moquírmti ofhmiofb k` dirnf f sfg`r qufb í f ipmomèi kis afgmtfot`s oi W`moi Pomki r`bftmvfn`ot` f qufb hiosmk`rfn s`r f n`bair gfokf grmtçomhf k` tikis is t`npis. @shiba`-s`, fi fhfsi, un moquírmti r`fbmzfki p`bf r`vmstf. X`lf F i fhiot`hmn`oti "f p`ssif moqumrmkf t`n ofhmiofbmkfk` mocb`sf", ` s`lf G i fhiot`hmn`oti "f p`ssif moqumrmkf s`b`hmioiu f gfokf [a` G`ftb`s ". Xfg`-s` qu`< • 15% kis
moqumrmkis moqumrmkis tìn ofhmiofbmkfk ofhmiofbmkfk`` mocb`sf: mocb`sf:
• `otr`
is moqumrmkis qu` oèi tìn ofhmiofbmkfk` mocb`sf, 6 `n hfkf 0 s`b`hmioiu is [a` G`ftb`s hini n`bair gfokf mocb`sf k` tikis is t`npis.
K`t`rnmo` U F| (F ∬ G ) .
Fpr`s`ot` i r`subtfki `n dirnf k` drfãèi mrr`kutîv`b.
. Oun
hbug` k` tr`moi `xmst`n værmfs ziofs k` tr`moi mohbumoki unf pmshmof ` unf sfbf k` nushubfãèi. Fh`rhf kis n`ngris k`ss` hbug`, sfg`-s` qu`< • i
oün`ri k` n`ngris qu` dr`qu`otf f pmshmof í un qufrti ki oün`ri k` n`ngris qu` dr`qu`otf f sfbf k` nushubfãèi: • i oün`ri k` n`ngris qu` dr`qu`otf f pmshmof iu f sfbf k` nushubfãèi í i kigri ki oün`ri k` n`ngris qu` oèi dr`qu`otf dr`qu`o tf o`oaunf o`oaunf k`ssfs ziofs: • `otr` is n`ngris qu` oèi dr`qu`otfn f sfbf k` nushubfãèi, un s`xti k`ss`s dr`qu`otfn f pmshmof.
i r m ` r r ` u C b ` u c m N i o u O •
n i h . t
@shiba`-s`, fi fhfsi, un n`ngri k`ss` hbug`. K`t`rnmo` f prigfgmbmkfk` k` `ss` n`ngri dr`qu`otfr f pmshmof. Fpr`s`ot` i r`subtfki of dirnf k` drfãèi mrr`kutîv`b.
f n s m f n b f o m s •
= 6 5 7
6;
©
Urigfgmbmkfk`s ` Hingmoftørmf • Nft`nætmhf F ‘ 67¼ foi
. F
NhBfr NhBfr`o `o D6 [`fn í unf `qumpf `qumpf gr grmtç mtçomh omhff k` futin futinigm igmbms bmsni ni qu` hinp`t hinp`t`` of Dørnubf Dørnubf 6. Kfs hirrmkf hirrmkfss `n qu` f `qumpf pfrtmhmpiu pfrtmhmpiu oi hmrhumti hmrhumti k` Xmbv`rstio`, Xmbv`rstio`, sfg`-s` qu`< • 7
`n hfkf 3 hirrmkfs oi hmrhumti t`rnmofrfn hin f vmtørmf k` un pmbiti kf NhBfr`o D6 [`fn:
• 6
`n hfkf 4 hirrmkfs hin`ãfrfn hin un pmbiti kf NhBfr`o D6 [`fn of pib` pismtmio :
• kfs
hirrmkfs qu` oèi t`rnmofrfn hin f vmtørmf k` un pmbiti kf NhBfr`o D6 [`fn, 6 `n hfkf 65 hin`ãfrfn hin un pmbiti k`ssf `qumpf of pib` pismtmio.
@shiba`-s`, fi fhfsi, unf hirrmkf oi hmrhumti k` Xmbv`rstio` qu` hin`ãiu hin un pmbiti kf NhBfr`o D6 [`fn of pib` pismtmio. Vufb í f prigfgmbmkfk` ki pmbiti t`r cfoai f hirrmkf9 Fpr`s`ot` i r`subtfki `n dirnf k` drfãèi mrr`kutîv`b. . Hmohi
fnmcis fnmcis vmsmtfrfn vmsmtfrfn Gukfp`st` oi v`rèi k` 756=. Pnf kfs ftrfãð`s dfvirmtfs dfvirmtfs ki crupi k` fnmcis `n Gukfp`st` dirfn is gfoais t`rnfms. W`bftmvfn`ot` å ihupfãèi k` unf kfs t`rnfs oun kfki kmf sfg`-s` qu`< • n`tfk` • `otr`
kis vmsmtfot`s vmsmtfot`s sèi `strfoc`mris `strfoc`mris::
is vmsmtfot`s qu` ouohf vmsmtmrfn fs t`rnfs fot`s, kims `n hfkf trìs sèi `strfoc`mris:
• quftri
`n hfkf hmohi vmsmtfot`s sèi `strfoc`mris iu læ tmoafn vmsmtfki fs t`rnfs fot`rmirn`ot`.
Í `shibamki, fi fhfsi, un vmsmtfot` kfs t`rnfs o`ss` kmf. Vufb f prigfgmbmkfk` k` ouohf fot`s t`r vmsmtfki fs t`rnfs9 Fpr`s`ot` i r`subtfki of dirnf k` drfãèi mrr`kutîv`b. . Pnf
`npr`sf t`hoibøcmhf pirtucu`sf `npr`cf 705 p`ssifs ois s`us `shrmtørmis `n Uirtucfb ` @stfkis Pomkis kf Fnírmhf. Fh`rhf kfs p`ssifs `npr`cfkfs o`ssf `npr`sf, sfg`-s` qu`< • 3
`n hfkf 65 `npr`cfkis kf `npr`sf trfgfbafn ois `shrmtørmis `n Uirtucfb:
• 7
`n hfkf 0 kis `npr`cfkis qu` trfgfbafn ois `shrmtørmis `n Uirtucfb sèi `strfoc`mris:
• 6
`n hfkf 1 kis `npr`cfkis pirtucu`s`s trfgfbafn ois `shrmtørmis ois @stfkis Pomkis kf Fnírmhf.
I K`ooms í un `npr`cfki su`hi k`stf `npr`sf t`hoibøcmhf. Vufb í f prigfgmbmkfk` ki K`ooms trfgfbafr ois `shrmtørmis `n Uirtucfb9 Fpr`s`ot` i r`subtfki of dirnf k` drfãèi mrr`kutîv`b.
. I
Ouoi ` i Tfshi r`cmstfrfn r`cmstfrfn is r`subtfkis r`subtfkis k` tikfs fs sufs pfrtmkfs pfrtmkfs k` tíoms kurfot` i foi k` 7561. 7561. @ssfs pfrtm pfrtmkfs kfs dirfn licfkfs `n pmsi ræpmki iu `n t`rrf gftmkf.
i r m ` r r ` u C b ` u c m N i o u O •
n i h . t f n s m f n b f o m s
Xfg`-s` qu`< • i
Ouoi v`oh`u trìs `n hfkf hmohi pfrtmkfs kmsputfkfs:
• i
Tfshi v`oh`u trìs `n hfkf hmohi pfrtmkfs kmsputfkfs `n t`rrf gftmkf:
• trìs
`n hfkf quftri pfrtmkfs qu` i Ouoi v`oh`u dirfn kmsputfkfs `n pmsi ræpmki.
Í `shibamkf, fi fhfsi, unf pfrtmkf kmsputfkf `otr` is kims fnmcis. Vufb í f prigfgmbmkfk` k`ssf pfrtmkf t`r smki kmsputfkf `n pmsi ræpmki9 Fpr`s`ot` i r`subtfki of dirnf k` drfãèi mrr`kutîv`b.
•
= 6 5 7
©
60
Urigfgmbmkfk`s ` Hingmoftørmf • Nft`nætmhf F ‘ 67¼ foi
. Hiosmk`r`
un sfhi hin qumoz` gibfs oun`rfkfs k` 6 f 60 ` kmstmocuîv`ms p`bf hir< k`z fnfr`bfs ` hmohi fzums. Xfg`-s` qu` fs k`z gibfs fnfr`bfs sèi oun`rfkfs k` 6 f 65 , ` fs gibfs fzums sèi oun`rfkfs k` 66 f 60 . Tèi s`r `xtrfîkfs, fi fhfsi, quftri gibfs ki sfhi. X`lf F i fhiot`hmn`oti "sèi `xtrfîkfs gibfs kf n`snf hir", ` s`lf G i fhiot`hmn`oti "tikfs fs gibfs `xtrfîkfs `stèi oun`rfkfs hin un oün`ri pfr". K`t`rnmo` i vfbir k` U ( ( F|G ), s`n r`hirr`r å dørnubf kf prigfgmbmkfk` hiokmhmiofkf. Lustmstqu` f suf r`spistf ounf hinpismãèi, `n qu` k`v`<
7
• `xpbmhfr
i smcomsthfki k` U ( F|G ) oi hiot`xti kf smtufãèi k`shrmtf:
• `xpbmhfr
i oün`ri k` hfsis pissîv`ms ` i oün`ri k` hfsis dfviræv`ms:
• fpr`s`otfr
0 \ \ \ ; \ \ 8 \ \ \ 6 \ \ \\\ f
g
h
k
`
i vfbir p`kmki of dirnf k` drfãèi mrr`kutîv`b.
. Pnf
hinpfoamf k` s`curis hbfssmsthf is s`us hbm`ot`s `n kufs hft`cirmfs< is hbm`ot`s prip`osis f fhmk`ot`s, ` is hbm`ot`s oèi prip`osis f fhmk`ot`s. fhmk`ot`s.
Xfg`-s` qu`< • 70% kis • 0% kis
hbm`ot`s k`ssf hinpfoamf tìn un fhmk`ot` oi p`rîiki k` hig`rturf ki s`curi:
hbm`ot`s oèi prip`osis f fhmk`ot`s tìn un fhmk`ot` oi p`rîiki k` hig`rturf ki s`curi:
• 15% kis
hbm`ot`s prip`osis f fhmk`ot`s tìn un fhmk`ot` oi p`rîiki k` hig`rturf ki s`curi.
@shiba`-s` fi fhfsi un hbm`ot` k`ssf hinpfoamf k` s`curis. Vufb í f prigfgmbmkfk` k`ss` hbm`ot` `stfr hft`cirmzfki hini prip`osi f fhmk`ot`s9 Fpr`s`ot` i r`subtfki of dirnf k` drfãèi mrr`kutîv`b. . Hiosmk`r`
unf turnf k` kíhmni s`cuoki foi hiostmtuîkf pir 6; rfpfz`s ` 65 rfpfrmcfs.
[ikis is fbuois kf turnf r`fbmzfrfn oi kíhmni prmn`mri foi i @xfn` Ofhmiofb k` C`in`trmf K`shrmtmvf iu i @xfn` Ofhmiofb k` Gmibicmf ` C`ibicmf. Xfg`-s` fmokf qu`< • 65 • 8
fbuois r`fbmzfrfn i @xfn` Ofhmiofb k` C`in`trmf K`shrmtmvf:
`n hfkf 3 fbuois qu` r`fbmzfrfn i @xfn` Ofhmiofb k` Gmibicmf ` C`ibicmf sèi rfpfz`s.
Vufb í f prigfgmbmkfk` k`, `shiba`oki un fbuoi kf turnf fi fhfsi, `ss` fbuoi s`r rfpfz iu t`r r`fbmzfki i @xfn` Ofhmiofbb k` C`in`trmf Ofhmiof C`in`trmf K`shrmtmvf9 K`shrmtmvf9 Fpr`s`ot` i r`subtfki of dirnf k` drfãèi mrr`kutîv`b. . X`lf @ un
hioluoti stomti, U unf prigfgmbmkfk` `n U (@ ) ` F, G ∁ U (@ ).
Xfg`-s` qu`< •
6 ;
≫ U (F|G) ≫ 76
• U (F
∭ G) > 06
•
Vufb kis s`cumot`s vfbir`s pik` s`r i vfbir k` U (G )9 (F)
6 65
i r m ` r r ` u C b ` u c m N i o u O
(G)
7 0
(H)
8 ;
(K)
; 0
n i h . t f n s m f n b f o m s •
= 6 5 7
64
©
Urigfgmbmkfk`s ` Hingmoftørmf • Nft`nætmhf F ‘ 67¼ foi
. I
Fotøomi ` i Tfshi r`cmstfrfn is r`subtfkis kfs 85 pfrtmkfs k` tíoms qu` kmsputfrfn oi übtmni v`rèi.
Xfg`-s` qu` tikis fs pfrtmkfs t`rnmofrfn hin f vmtørmf ki Fotøomi iu ki Tfshi, s`oki qu` i Tfshi v`oh`u 45% kfs pfrtmkfs kmsputfkfs, ` `otr` fs qu` i Fotøomi v`oh`u 05% dirfn k`hmkmkfs `n tm`-gr`fj . Vufotfs pfrtmkfs t`rnmofrfn hin f vmtørmf ki Fotøomi ` oèi dirfn k`hmkmkfs `n tm`-gr`fj 9 (F) 8 . Hiosmk`r`
(G) 4
(H) =
(K) 67
un crupi k` kiz` fnmcis hiostmtuîki pir imti rfpfrmcfs ` quftri rfpfz`s, `otr` is qufms `stèi i Fotøomi `
i Tfshi. Tfm s`r dirnfkf unf hinmssèi k` quftri p`ssifs `otr` is kiz` fnmcis. Tfm s`r `shibamkf, fi fhfsi, unf hinmssèi `otr` tikfs fs hinmssð`s pissîv`ms. X`lf F i fhiot`hmn`oti "f hinmssèi t`n, p`bi n`ois, trìs rfpfz`s"` G i fhiot`hmn`oti "i Fotøomi ` i Tfshi dfz`n pfrt`` kf hinmssèi". pfrt hinmssèi". K`t`rnmo` i vfbir k` U (G |F), hin`ãfoki pir `xpbmhfr i smcomsthfki k` U (G |F) oi hiot`xti ki prigb`nf. Fpr`s`ot` i r`subtfki of dirnf k` p`rh`otfc`n, hin frr`okiokfn`oti ås kíhmnfs. . Of
Dmcurf fgfmxi `stæ r`pr`s`otfki un tfgub`mri hin vmot` ` hmohi hfsfs.
0 \ \ \ p`ãfs pr`tfs. ; X`lf F i fhiot`hmn`oti "fs p`ãfs k` unf kfkf hir ihupfn unf hibuof ki tfgu \ \ 8 b`mri", ` s`lf G i fhiot`hmn`oti "fs p`ãfs k` unf kfkf hir ihupfn unf kmfciofb ki \ \ \ tfgub`mri". 7 \ \ Mokmqu` i vfbir k` U (G |F), s`n utmbmzfr f dørnubf dørnubf kf prigfgmbmk prigfgmbmkfk` fk` hiokmhmiofk hiokmhmiofkf. f. 6 \ \ \ Lustmstqu` f suf r`spistf, hin`ãfoki pir `xpbmhfr i smcomsthfki k` U (G |F) oi hioHiosmk`r` tikfs fs kmspismãð`s pissîv`ms oi tfgub`mri kfs s`ms p`ãfs grfohfs ` kfs imti
t`xti kf smtufãèi smtufãèi k`shrmtf. k`shrmtf. . Hiosmk`r`
f
g
h
k
`
f bmoaf 6; ki [rmçocubi k` Ufshfb.
Tèi s`r `shibamkis, suh`ssmvfn`ot` ` fi fhfsi, kims `b`n`otis k`ssf bmoaf. X`lf F i fhiot`hmn`oti "is kims `b`n`otis `shibamkis tìn vfbir nfmir qu` 6;H 0 ", ` G i fhiot`hmn`oti "i prikuti kis `b`n`otis `shibamkis í n`oir iu mcufb f 6; ". @shr`vf f `xpr`ssèi qu` p`rnmt` k`t`rnmofr i vfbir k` U (G |F), hin`ãfoki pir `xpbmhfr i smcomsthfki k` U (G |F) oi hiot`xti ki prigb`nf.
. I i r m ` r r ` u C b ` u c m N i o u O •
n i h . t f n s m f n b f o m s
U`kri ` i Cum r`cmstfrfn is r`subtfkis kis 70 licis k` dut`gib qu` kmsputfrfn oi stn-k`-s`nfof of UX; .
Xfg`-s` qu`< • i
U`kri v`oh`u 60 licis ` i Cum v`oh`u is r`stfot`s: • 6 `n hfkf 8 licis qu` i U`kri v`oh`u t`rnmofrfn hin unf vfotfc`n sup`rmir f kims cibis: • r`cmstfrfn-s` 1 licis `n qu` i U`kri oèi v`oh`u ` f vfotfc`n ki v`oh`kir oèi dim sup`rmir f kims cibis. Hiosmk`r` qu` dim `shibamki un lici fi fhfsi `otr` is qu` t`rnmofrfn hin unf vfotfc`n ki v`oh`kir sup`rmir f kims cibis. Vufb f prigfgmbmkfk` ki Cum t`r v`ohmki `ss` lici9 Fpr`s`ot` i r`subtfki `n dirnf k` drfãèi mrr`kutîv`b.
•
= 6 5 7
©
63
Urigfgmbmkfk`s ` Hingmoftørmf • Nft`nætmhf F ‘ 67¼ foi
. X`lf @ un
hioluoti stomti, U unf prigfgmbmkfk` `n U (@ ) ` F, G ∁ U (@ ). Xfg`-s` qu`< • F ` G sèi
`qumprivæv`ms:
∬ G) > 08 6 • U (F|G ) > 8 • U (F
Vufb i vfbir k` U (F ∬ G ) 9 6 7
(F)
(G)
8 0
(H)
3 65
(K)
; 0
. Hiosmk`r`
i mocr`ssi oi hursi k` @oc`oafrmf Modirnætmhf ` k` Hinputfkir`s ki Mostmtuti Xup`rmir [íhomhi oi foi b`tmvi k` 7561/756=. Xfg`-s` qu`< • ;
`n hfkf 0 fbuois qu` mocr`ssfrfn oi hursi sèi rfpfz`s:
• =
`n hfkf 65 fbuois qu` mocr`ssfrfn oi hursi tmv`rfn oitf sup`rmir f 61 vfbir`s oi @xfn` Dmofb Ofhmiofb k` Nft`nætmhf F:
• 45% kis
fbuois qu` oèi tmv`rfn oitf sup`rmir f 61 vfbir`s oi @xfn` Dmofb Ofhmiofb k` Nft`nætmhf F sèi rfpfrmcfs.
I Tfshi í un kis fbuois qu` mocr`ssiu oi hursi oi foi b`tmvi k` 7561/756=. Vufb f prigfgmbmkfk` k` t`r tmki oitf sup`rmir f 61 vfbir`s oi @xfn` Dmofb Ofhmiofb k` Nft`nætmhf F 9 Fpr`s`ot` Fpr`s `ot` i r`subtfki r`subtfki `n p`rh`otfc`n. p`rh`otfc`n. . I
Nmcu`b ` f B`ioir sèi is üomhis trfgfbafkir`s k` un k`pfrtfn`oti k` unf kfkf `npr`sf.
@shibaf-s`, fi fhfsi, un r`bftørmi r`fbmzfki p`bi k`pfrtfn`oti iok` trfgfbafn i Nmcu`b ` f B`ioir. X`lf F i fhiot`hmn`ot fhiot`hmn`otii «i r`bftørmi r`bftørmi `shibamki `shibamki í kf r`spiosfgmbm r`spiosfgmbmkfk` kfk` ki Nmcu`bº Nmcu`bº, ` s`lf G i fhiot`hmn`oti «i r`bftørmi `shibamki dim g`n `x`hutfkiº. Xfg`-s` qu`< • i
Nmcu`b ` f B`ioir sèi r`spiosæv`ms p`bi n`sni oün`ri k` r`bftørmis:
• =3 `n • 6 `n
hfkf 655 r`bftørmis sèi kf r`spiosfgmbmkfk` ki Nmcu`b iu sèi g`n `x`hutfkis:
hfkf 70 r`bftørmis kf r`spiosfgmbmkfk` ki Nmcu`b oèi sèi g`n `x`hutfkis.
K`t`rnmo` U (G ), fpr`s`otfo fpr`s`otfoki ki i r`subtfki r`subtfki `n p`rh`otfc`n. p`rh`otfc`n.
. @n
oiv`ngri k` 7561 k`hirr`ræ, k`hirr`ræ, `n Bmsgif, Bmsgif, un `ohiotri `ohiotri mot`rofhmiofb mot`rofhmiofb k` `sp`hmfbmstfs `sp`hmfbmstfs ki s`tir f`ri`spfhmfb. f`ri`spfhmfb. i r m ` r r ` u C b ` u c m N i o u O
Kis `sp`hmfbmstfs pr`s`ot`s oi hiocr`ssi sfg`-s` qu`< • trìs • un
`n hfkf hmohi `sp`hmfbmstfs sèi aibfok`s`s:
`n hfkf trìs aibfok`s`s oèi í `oc`oa`mri:
• quftri
`n hfkf hmohi `oc`oa`mris sèi aibfok`s`s.
@shiba`u-s`, @shiba` u-s`, fi fhfsi, un `sp`hmfbmstf `sp`hmfbmstf pr`s`ot` pr`s`ot` oi hiocr`ssi. K`t`rnmo` f prigfgmbmkfk` k`ss` `sp`hmfbmstf s`r aibfokìs iu s`r `oc`oa`mri. Fpr`s`ot` i r`subtfki of dirnf k` drfãèi mrr`kutîv`b.
•
n i h . t f n s m f n b f o m s •
= 6 5 7
61
©
Urigfgmbmkfk`s ` Hingmoftørmf • Nft`nætmhf F ‘ 67¼ foi
. Pn
bfgirftørmi bfgirftørmi k` gmibicmf gmibicmf k`s`ovibv`u k`s`ovibv`u un prikuti prikuti pfrf n`bairfr n`bairfr f sfük` kis p`mx`s k` un kfki rmi. Ufrf Ufrf t`stæ-bi dim r`hibamkf unf fnistrf kf æcuf hiotfnmofkf, t`oki smki mos`rmkis 055 p`mx p`mx`s `s ki rmi o`ssf æcuf. I prikuti prikuti dim `otèi hibihfki of æcuf, ` fv`rmciu-s` s` i n`sni dim g`oísthi iu nfbmcoi pfrf f sfük` kis p`mx`s. Fpøs is t`st`s, v`rmsthiu-s` qu`< • 45% kis
p`mx`s k`ssf æcuf `stfvfn hiotfnmofkis p`bi vîrus:
• i
prikuti dim g`oísthi pfrf f sfük` k` =0% kis p`mx`s hiotfnmofkis p`bi vîrus:
• i
prikuti dim nfbmcoi pfrf f sfük` k` 6% kis p`mx`s oèi hiotfnmofkis p`bi vîrus.
F fknmomstrfãèi ki prikuti dim g`oísthf pfrf qufotis p`mx`s k`ssf fnistrf9
. X`lf @ un
hioluoti stomti, U unf prigfgmbmkfk` `n U (@ ) ` F, G ∁ U (@ ), hin U (G ) > 5.
Nistr` qu` U (F|G ) ∗ U (F|G ) . X`lf @ un
Ó
U (G ) + U (F) > U (F G ).
|
hioluoti stomti, U unf prigfgmbmkfk` `n U (@ ) ` F, G ∁ U (@ ).
Xfg`-s` qu`< • U (F) > • U (F
8 0
G) >
6
| 8 ∬ G) > 0;
• U (F
Vufb i vfbir k` U (F|G ) 9 . K`
un hursi k` `oc`oafrmf `oc`oafrmf `b`tritíhomhf `b`tritíhomhf ` hinputfkir`s hinputfkir`s k` unf `shibf pirtucu`sf pirtucu`sf sfg`-s` qu`<
• 3 `n
hfkf 65 fbuois `shiba` f ær`f hm`otîsthf k` hiotribi k` smst`nfs, ` is r`stfot`s `shiba`n f ær`f hm`otîsthf k` hinputfkir`s:
• 6 `n
hfkf 1 fbuois k`ss` hursi oèi `stèi sftmsd`mtis hin f qufbmkfk` ki `osmoi of ær`f qu` `shiba`rfn:
• = `n
hfkf 65 fbuois qu` `shiba`n f ær`f k` hiotribi k` smst`nfs, `stèi sftmsd`mtis hin f qufbmkfk` ki `osmoi of
ær`f. I Gruoi í un fbuoi k`ss` hursi ` `stæ sftmsd`mti hin f qufbmkfk` ki `osmoi of ær`f qu` `shiba`u. Vufb f prigfgmbmkfk` k` t`r `shibamki f ær`f hm`otîsthf k` hinputfkir`s9 Fpr`s`ot` i r`subtfki hin frr`kiokfn`oti ås h`otísmnfs.
i r m ` r r ` u C b ` u c m N i o u O •
n i h . t f n s m f n b f o m s
. X`lf @ un
hioluoti stomti, U unf prigfgmbmkfk` `n U (@ ) ` F, G ∁ U (@ ).
Xfg`-s` qu`<
• F ` G sèi • U (F) > • U (G )
mohinpftîv`ms:
5,;
> 5 ,8
Vufb i vfbir k` U (G F)9 (F) 5,8
|
(G) 5,;
(H) 5,0
(K) 5,4
•
= 6 5 7
©
6=
Urigfgmbmkfk`s ` Hingmoftørmf • Nft`nætmhf F ‘ 67¼ foi
. Pn
sfhi hiotín oiv` gibfs hibirmkfs oun`rfkfs k` 6 f = , mokmstmocuîv`ms fi tfti, tfms qu`<
• fs
gibfs oun`rfkfs k` 6 f 8 sèi fnfr`bfs:
• fs
gibfs oun`rfkfs k` ; f 4 sèi v`rn`bafs:
• fs
gibfs oun`rfkfs k` 3 f = sèi fzums.
Dirfn fkmhmiofkfs fi sfhi o gibfs înpfr`s fnfr`bfs. Hiosmk`r` f `xp`rmìohmf fb`ftørmf qu` hiosmst` `n r`tmrfr kufs gibfs, fi fhfsi ` s`n r`pismãèi, ki sfhi ` igs`rvfr fs r`sp`tmvfs hir`s ` oün`ris. r`sp`tmvfs oün`ris. X`lfn F ` G is fhiot`hmn`otis< F< "Of prmn`mrf `xtrfãèi í r`tmrfkf unf gibf înpfr v`rn`baf" G < "I prikuti kis oün`ris r`tmrfkis í pfr ` fs gibfs r`tmrfkfs sèi k` hir`s kmd`r`ot`s"
Mokmqu` i vfbir k` U (G |F), `n duoãèi k` o, s`n utmbmzfr f dørnubf dørnubf kf prigfgmbmk prigfgmbmkfk` fk` hiokmhmiofkf. hiokmhmiofkf. Lustmstqu` f suf r`spistf, hin`ãfoki pir `xpbmhfr i smcomsthfki k` U (G |F) oi hiot`xti kf smtufãèi k`shrmtf. . I
[inæs d`z unf foæbms` fi hirr`mi qu` t`n ha`cfki fi s`u nfmb, ` hiostftiu qu` 65% kis `nfmbs qu` r`h`g` sèi kmr`hmiofkis pfrf f hfmxf k` spfn. Ufrf fbín kmssi oitiu qu`< • kfs
n`osfc`os qu` sèi kmr`hmiofkfs pfrf f hfmxf k` spfn, 45% tìn vîrus: • 8 `n hfkf 70 n`osfc`os sèi kmr`hmiofkfs pfrf f hfmxf k` spfn iu tìn vîrus.
@shiba`-s`, fi fhfsi, unf n`osfc`n qu` t`n vîrus. Vufb f prigfgmbmkfk` kf n`osfc`n oèi t`r smki kmr`hmiofkf pfrf f hfmxf k` spfn9 Fpr`s`ot` i r`subtfki of dirnf k` drfãèi mrr`kutîv`b.
. X`lf @ un
hioluoti stomti, U unf prigfgmbmkfk` `n U (@ ) ` F, G ∁ U (@ ).
Xfg`-s` qu`< • U (G )
> 5 ,1
• U (F
|G) > 5 ,0 • U (F ∬ G ) > 5,=
Vufb í i vfbir k` U (F) 9 5 ,6 (F) 5 (F)
. Pn
(G) 5 (G) 5 ,0
(H) 5 (H) 5 ,1
(K) 5 (K) 5 ,=
quînmhi vfm r`fbmzfr un t`st` k` dirnf f fv`rmcufr f hiotfnmofãèi k` æcuf pir sugstçohmfs quînmhfs.
Xfg`-s` qu`< • qufoki
`ssfs sugstçohmfs quînmhfs `stèi pr`s`ot`s of æcuf, i quînmhi k`t`tf f pr`s`oãf kfs n`snfs `n =1% kis t`st`s: • qufoki fs sugstçohmfs quînmhfs oèi `stèi pr`s`ot`s of æcuf, i quînmhi mk`otmsthf f pr`s`oãf kfs n`snfs `n 7% kis t`st`s: • f prigfgmbmkfk` k` unf fnistrf k` æcuf `stfr hiotfnmofkf pir sugstçohmfs quînmhfs í 0%
K`t`rnmo` f prigfgmbmkfk` ki quînmhi gèi k`t`tfr f pr`s`oãf kfs sugstçohmfs ` `stfs sugstçohmfs oèi `stfr`n pr`s`ot`s of æcuf. Fpr`s`ot` i r`subtfki of dirnf k` p`rh`otfc`n hin frr`kiokfn`oti ås kíhmnfs.
i r m ` r r ` u C b ` u c m N i o u O •
n i h . t f n s m f n b f o m s •
= 6 5 7
75
©
Urigfgmbmkfk`s ` Hingmoftørmf • Nft`nætmhf F ‘ 67¼ foi
. X`lf @ un
hioluoti stomti, U unf prigfgmbmkfk` `n U (@ ) ` F, G ∁ U (@ ).
Xfg`-s` qu`< • U (F
∭ G) > 5,7 • U (F|G ) > 5 ,0 Vufb í i vfbir k` U (G )9 (F) 5 (F) 5 ,8
. X`lf @ un
(G) 5 (G) 5 ,;
(H) 5 (H) 5 ,0
(K) 5 (K) 5 ,4
hioluoti stomti, U unf prigfgmbmkfk` `n U (@ ) ` F, G ∁ U (@ ).
Xfg`-s` qu`< • U (F) > • U (G
5,7
|F) > U (F|G)
Vufb í i vfbir k` U (G )9 5 ,7 (F) 5 (F)
. X`lf @ un
(G) 5 (G) 5 ,;
(H) 5 (H) 5 ,4
(K) 5 (K) 5 ,1
hioluoti stomti, U unf prigfgmbmkfk` `n U (@ ) ` F, G ∁ U (@ ).
Xfg`-s` qu`< • U (F) > • U (G
5,4
|F) > 5 ,0
Vufb í i vfbir k` U (F ∬ G )9 (F) 5 (F) 5 ,0
. K`
(G) 5 (G) 5 ,4
(H) 5 (H) 5 ,3
(K) 5 (K) 5 ,1
unf `qumpf k` dut`gib pirtucu`sf hin 75 licfkir`s, sfg`-s` qu`<
• 7
`n hfkf 0 licfkir`s kf `qumpf tìn ofhmiofbmkfk` pirtucu`sf:
• 70% kis
licfkir`s kf `qumpf tìn n`ois k` 76 fois k` mkfk`:
• 75% kis
licfkir`s hin n`ois k` 76 fois k` mkfk` oèi tìn ofhmiofbmkfk` pirtucu`sf.
@shiba`-s`, @shiba` -s`, fi fhfsi, un licfkir licfkir k`ssf `qumpf hin ofhmiofbmkfk` ofhmiofbmkfk` pirtucu`sf. pirtucu`sf. Vufb í f prigfgmbmkfk` k`ss` licfkir t`r n`ois k` 76 fois k` mkfk`9
i r m ` r r ` u C b ` u c m N i o u O •
n i h . t f n s m f n b f o m s
. I
U`kri ` i Dmbmp` vèi vmflfr kurfot` fbcuos kmfs f Fn`st`rkèi.
Xfg`-s` qu`< • o`viu • i
`n Fn`st`rkèi `n 45% kis kmfs `n qu` i U`kri ` i Dmbmp` bæ `stmv`rfn:
U`kri ` i Dmbmp` fbucfrfn gmhmhb`tfs pfrf pfss`fr p`bf hmkfk` `n 15% kis kmfs `n qu` o`viu `n Fn`st`rkèi:
• oèi
o`viu `n Fn`st`rkèi `n ;5% kis kmfs `n qu` i U`kri ` i Dmbmp` fbucfrfn gmhmhb`tfs pfrf pfss`fr p`bf hmkfk`.
K`t`rnmo` f prigfgmbmkfk` k`, `shibamki un kmf kf vmfc`n fi fhfsi, i U`kri ` i Dmbmp` oèi fbucfr`n gmhmhb`tfs pfrf pfss`frr p`bf hmkfk`. pfss`f
•
= 6 5 7
©
76
Urigfgmbmkfk`s ` Hingmoftørmf • Nft`nætmhf F ‘ 67¼ foi
. Hiosmk`r`
kims sfhis, F ` G . I sfhi F t`n quftri gibfs v`rn`bafs v`rn`bafs ` trìs gibfs fzums. I sfhi G t`n trìs gibfs v`rn`bafs ` o (o ∁ O) gibfs fzums.
Hiosmk`r` f `xp`rmìohmf qu` hiosmst` `n r`tmrfr, smnubtfo`fn`ot` ` fi fhfsi, trìs gibfs ki sfhi F , ` hfsi • s`lfn • oèi
`xtrfîkfs trìs gibfs kf n`snf hir, `ssfs n`snfs gibfs sèi hibihfkfs oi sfhi G .
s`lfn `xtrfîkfs trìs gibfs kf n`snf hir, `ssfs n`snfs gibfs sèi r`pistfs oi sfhi F.
X`lfn F ` G is fhiot`hmn`otis< F < "fs trìs gibfs r`tmrfkfs ki sfhi F sèi fzums" G < "f gibf r`tmrfkf ki sfhi G í fzub"
Xfg`-s` U (G |F) >
0 . 1
K`t`rnmo` i vfbir k` o.
. Oi
r`d`r`ohmfb i.o x Iy kf stcurf, `stæ r`pr`s`otf r`pr`s`otfki ki un ihtøcioi ihtøcioi r`cubfr Z FGHK@DCA ^ moshrmti ounf hmrhuod`rìohmf. y H G K F x @ A D C
Hiosmk`r` is trmçocubis r`pr`s`otfkis of stcurf qu` uo`n f irmc`n f kims vírtmh`s hios`hutmvis ki ihtøcioi. I [mfci t`n quftri hir`s pfrf hibirmr is trmçocubis, `otr` fs qufms `stèi f hir fzub ` f hir v`rn`baf. Hiosmk`r` is fhiot`hmn`otis< F< "; trmçocubis sthfn pmotfkis hin hir v`rn`baf ` ; trmçocubis sthfn pmotfkis hin hir fzub" G < "; trmçocubis sthfn pmotfkis hin unf kfkf hir, ` is iutris ; hin unf iutrf"
K`t`rnmo` i vfbir k` U (F|G ), s`n utmbmzfr utmbmzfr f dørnubf dørnubf kf prigfgmbm prigfgmbmkfk` kfk` hiokmhmiofkf. hiokmhmiofkf. . Hiosmk`r`
f `xp`rmìohmf fb`ftørmf qu` hiosmst` `n `d`tufr kims bfoãfn`otis kun kfki r`cubfr oun`rfki k` 6 f 4.
X`lfn F ` G is fhiot`hmn`otis< F< "f sinf kis oün`ris sfîkis í nfmir iu mcufb f =" G < "i oün`ri 0 sfm oi prmn`mri bfoãfn`oti"
i r m ` r r ` u C b ` u c m N i o u O •
Vufb i vfbir kf prigfgmbmkfk` U (F|G )9 (F)
6 8
(G)
7 8
(H)
6 7
(K)
n i h . t f n s m f n b f o m s
8 ;
•
= 6 5 7
77
©
Urigfgmbmkfk`s ` Hingmoftørmf • Nft`nætmhf F ‘ 67¼ foi
. [`oaf
`n hiotf unf hfmxf qu` hiotín 4 gibfs, mokmstmocuîv`ms fi tfhti, oun`rfkfs k` 6 f 4.
Hiosmk`r` f `xp`rmìohmf fb`ftørmf qu` hiosmst` `n r`tmrfr smnubtfo`fn`ot` 7 gibfs kf hfmxf ` is fhiot`hmn`otis< F < "i prikuti kis oün`ris kfs gibfs í pfr" G < "i prikuti kis oün`ris kfs gibfs í n`oir iu mcufb f ;"
K`t`rnmo` i vfbir k` U (F|G ), s`n fpbmhfr fpbmhfr f dørn dørnubf ubf kf prigfgmbm prigfgmbmkfk` kfk` hiokmhmiofkf. hiokmhmiofkf. Of suf r`spistf< i smcomsthfki k` U (F|G ), oi hiot`xti kf smtufãèi k`shrmtf: • `xpbmqu` is hfsis pissîv`ms ` is hfsis dfviræv`ms: • `xpbmqu`
• fpr`s`ot`
i vfbir p`kmki.
. Ounf
kfkf dfhubkfk`, is fbuois pik`n mocr`ssfr oi pricrfnf @rfsnus `n qu` `st`s vèi `stukfr pfrf i `strfoc`mri kurfot` un kfki p`rîiki k` t`npi. Xfg`-s` qu`< • 35% kis
`stukfot`s iptf pir r`fbmzfr i pricrfnf k` @rfsnus oun pfîs `urip`u:
• 40% kis
`stukfot`s qu` r`fbmzfn i pricrfnf hiohbu`n hin suh`ssi tikfs fs uomkfk`s hurrmhubfr`s:
• 45% kis
`stukfot`s qu` oèi hiohbu`n hin suh`ssi tikfs fs uomkfk`s hurrmhubfr`s `stèi f r`fbmzfr i pricrfnf dirf kf @uripf.
I Fdiosi í un fbuoi k`stf dfhubkfk` dfhubkfk` ` `stæ f `stukfr `stukfr of Fb`nfoaf. Vufb f prigfgmbmkfk` prigfgmbmkfk` k`b` hiohbumr hiohbumr hin suh`ssi tikfs fs uomkfk`s uomkfk`s hurrmhubfr hurrmhubfr`s9 `s9 Fpr`s`ot` i r`subtfki of dirnf k` p`rh`otfc`n.
Hiosmk`r` . Hiosmk`r`
kufs hfmxfs hiostmtuîkfs hiostmtuîkfs pir gibfs mokmstmocuîv mokmstmocuîv`ms `ms fi tfhti. F hfmxf F hiotín 8 gibfs oun`rfkfs k` 6 f 8 ` f hfmxf G hiotín hiotín ; gibfs oun`rfkfs k` ; f 3.
[`oki `n hiotf f `xp`rmìohmf fb`ftørmf qu` hiosmst` `n bfoãfr un kfki r`cubfr hin dfh`s oun`rfkfs k` 6 f 4 `, s`cumkfn`ot`, hfsi f dfh` vibtfkf pfrf hmnf r`pr`s`ot` un oün`ri n`oir qu` 8 r`tmrfn-s` kufs gibfs kf hfmxf F, ` hfsi hiotrærmi, r`tmrfn-s` kufs gibfs kf hfmxf G . Hiosmk`r` is fhiot`hmn`otis< F< "f dfh` vibtfkf pfrf hmnf fpr`s`otf i oün`ri 4" G < "i prikuti kis oün`ris priv`om`ot`s kfs gibfs í pfr"
Vufb í i vfbir kf prigfgmbmkfk` U (G |F)9 (F)
6 4
(G)
6 8
(H)
0 4
(K)
7 8
i r m ` r r ` u C b ` u c m N i o u O •
n i h . t f n s m f n b f o m s •
= 6 5 7
©
78
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