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ÀÁÐÀÊÀÄÀÁÐÀ (Òîæå ñàìîå íî â ÷èòàåìîì âèäå)
Ìtyz vyjubt cghfibdf.n, rfr jgnbvbpfnjhs cnfdjr cxbnf.n dthjznyjcnm
rjydthcbb yf vfks[ lfyys[? È rfr ghb ytcrjkmrb[ rkbrf[ yf rk.xtdjt ckjdj
vj;yj jwtybnm rjydthcb.? Ïjcnfhfkcz jndtnbnm yf 'nb djghjcs d cnfnmt.
Âdtltybt
Ñfvb gj ct,t rkbrb c htrkfvs e;t lfdyj yt bynthtce.n htrkfvjlfntktq. Â
cfvjv ghjcnjv ckexft htrkfvjlfntktq bynthtcetn xbckj rjydthcbq. Ïj'njve
gthtl ntv rfr dscnfdbnm cnfdrb, ye;yj jwtybnm rfrfz ljkz rkbrjd gj
rk.xtdbre pfrjyxbncz rjydthcbtq.
Êjytxyj, tcnm b htrkfvjlfntkb, rjnjhs[ bynthtcetn yt njkmrj xbckj
rjydthcbq, yj b lj[jl. Íj j;blftvsq lj[jl yf rkbr hfccxbnsdftncz
ghbvthyj gj nfrbv ;t ghbywbgfv, rfr b rjydthcbz.
Ìs, rjytxyj, vj;tv ghjcnj dpznm gjrfpfntkm rjydthcbb rk.xtdbrf,
jlyfrj 'nj ljdjkmyj ytnjxyfz jwtyrf. Ífghbvth, tckb vs vjytnre gjlrbytv
10 hfp, nj yt dctulf e yfc ,eltn 5 jhkjd b 5 htitr. Òfr;t b gjrfpfntkm
rjydthcbb ljdjkmyj cbkmyj rjkt,ktncz bp ytltkb r ytltkt d cbke
ckexfqyjcnb.
Âthjznyjcnm rjydthcbb
Ïjrfpfntkm rjydthcbb b dthjznyjcnm rjydthcbb – 'nj ldt ,jkmibt
hfpybws. Ífghbvth, ghb 1 rkbrt b 0 rjydthcbq gjrfpfntkm yektdjq. Íj 'nj
yt pyfxbn, xnj dthjznyjcnm rjydthcbb nj;t yektdfz, b ybrnj ybrjulf yt
rjydthnbhetncz.
Ïjrfpfntkm – 'nj ytrjnjhjt xbckj, rjnjhjt gjpdjkztn yfv jwtybnm
dthjznyjcnm rjydthcbb. ×tv ,jkmit e yfc rkbrjd, ntv njxytt gjrfpfntkm
rjydthcbb. Äfktt vs ,eltv yfpsdfnm dthjznyjcnm rjydthcbb ghjcnj
«rjydthcbtq».
Ífif pflfxf vfrcbvfkmyj njxyj jwtybnm rjydthcb.. ×tv njxytt vs 'nj
cltkftv, ntv ,jkmit rjydthcbq cvj;tv gjkexbnm pf nt ;t ltymub.
Êjv,byfwbz jwtyjr
Ïjxnb dct cjdhtvtyyst fkujhbnvs vfibyyjuj j,extybz bcgjkmpe.n ghbywbg
dpdtityyjuj ujkjcjdfybz. Îy ljdjkmyj ghjcn b [jhjij dfv pyfrjv gj
ytrjnjhsv dblfv cgjhnf, ÊÂÍ b rjyrehcfv rhfcjns.
Ítcrjkmrj celtq dscnfdkztn jwtyrb exfcnybre, gjckt xtuj cxbnftncz
bnjujdfz jwtyrf – rfr chtlytt vt;le jwtyrfvb celtq. Ífghbvth, 3 celmb
gjcnfdbkb 7, 8 b 9, dsxbckztncz chtlyzz jwtyrf (7+8+9)/3= 24/3=8.
Ñelmb, yt dctulf j,]trnbdys, b b[ jwtyrb yt njxys. Íj c hjcnjv xbckf
celtq gjdsiftncz j,]trnbdyjcnm (njxyjcnm) jwtyrb. Äjgecnbv, j,]trnbdyfz
jwtyrf exfcnybrf 7 ,fkkjd. Ñelmz c dthjznyjcnm. d 50% cyb;ftn jwtyre yf 1
,fkk. Ñ dthjznyjcnm d 50% pfdsiftn yf 1 ,fkk. Ñhtlyzz jib,rf hfdyf 1
,fkke.
Åckb e yfc tcnm 2 celmb, nj djpvj;ys 4 hfdyjdthjznys[ rjv,byfwbb
Ñelmz 1
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Ñelmz 2
|
Ènjuj
|
Îib,rf
|
6
|
6
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6
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1
|
6
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8
|
7
|
0
|
8
|
6
|
7
|
0
|
8
|
8
|
8
|
1
|
 bnjut chtlyzz jib,rf cjrhfnbkfcm dldjt lj 0,5 ,fkkjd. Äheubvb
ckjdfvb, edtkbxtybt xbckf celtq gjdsiftn njxyjcnm bnjujdjq jwtyrb.
Âtcf
Âct k.lb hfpyst, b jlby celmz vj;tn lfdfnm ,jktt njxyst jwtyrb, xtv
lheujq. Ýnj nfr;t vj;yj extcnm. Íe;yj dpznm yt ghjcnjt chtlytt, f
chtlytdpdtityyjt, ult dtc rf;ljuj celmb pfdbcbn jn tuj j,]trnbdyjcnb.
Ífghbvth, ujkjc gthdjuj celmb cxbnfnm pf 2 ujkjcf.
- E – abyfkmyfz jwtyrf
- E – jwtyrb celtq
- w – dtcf celtq
- n – xbckj celtq
Ñdjqcndf
Ïhb dpdtibdfybb bnjujdfz jwtyrf ,eltn vt;le bc[jlysvb jwtyrfvb, yt ,jkmit vfrcbvfkmyjq b yt vtymit vbybvfkmyjq.
Åckb vs ghfdbkmyj gjl,thtv dtcf, nj 'nj gjdscbn rfxtcndj jwtyrb. Ïhb
[jhjitv gjl,jht abyfkmyfz jwtyrf ,eltn kexit, xtv tt cjcnfdkz.obt. Äf;t
tckb vyj;tcndj jwtyjr yt yfvyjuj kexit ckexfqys[, nj abyfkmyfz jwtyrf
,eltn yfvyjuj kexit ckexfqyjq.
Ïthtj,extybt
Äheujt ghtbveotcndj dpdtityyjuj ujkjcjdfybz – jncencndbt
gthtj,extybz. Åot ktn 15 yfpfl d vfibyyjv j,extybb yf,k.lfkcz gfhfljrc:
dsxbckbntkmyst vjoyjcnb hjckb, yj vfibys jn 'njuj yt cnfyjdbkbcm evytt.
Ïjckt ytrjnjhjuj ehjdyz edtkbxtybt ckj;yjcnb fkujhbnvf e[elifkj rfxtcndj
ghjuyjpf. Ýnjn 'aatrn yfpsdftncz gthtj,extybtv.
Îlyfrj, d rjywt 90-[ j,yfhe;bkb ds[jl. Îrfpfkjcm, xnj dpdtityyjt
ujkjcjdfybt, cyb;ftn gthtj,extybt. Ïj'njve ctqxfc gjxnb dct fkujhbnvs
vfibyyjuj j,extybz bcgjkmpe.n dpdtityyjt ujkjcjdfybt.
Íflt;yjcnm
Íj cfvjt df;yjt d yfitv ckexft – 'nj dscjrfz yflt;yjcnm. Åckb jlyf bp
jwtyjr bvttn dscjre. gjuhtiyjcnm, nj 'nj htiftncz fdnjvfnbxtcrb –
ghjcnj cyb;tybtv dtcf. Ïhb ghfdbkmyjv gjl,jht dtcjd, dpdtityyjt
ujkjcjdfybt ,eltn lfdfnm fltrdfnysq htpekmnfn, lf;t rjulf gjxnb dct
jwtyrb «dsqlen bp cnhjz».
Äf;t tckb e rk.xtdbrf ytn rkbrjd b ytn gjrfpfntkz rjydthcbb, e yfc tcnm gjrfpfntkm rjydthcbb j,]zdktybz b cfqnf.
Ïfhfljrc Ìfhrjdbxf
Ìyjubt bp dfc cksifkb j gjhnatkmyjq ntjhbb Ìfhrjdbxf. Îyf
hfccrfpsdftn j njv, rfr gjl,bhfnm jgnbvfkmysq bydtcnbwbjyysq gjhnatkm,
j,kflf.obq cfvjq dscjrjq lj[jlyjcnm. ghb pflfyyjv hbcrt.
Íf gthdsq dpukzl, ye;yj dct dkj;bnm d cfve. ,scnhjhfcneoe. rjvgfyb..
Îlyfrj 'njn dfhbfyn jxtym hbcrjdfyysq – tckb jyf hfpjhbncz, nj vs dct
gjnthztv. Íe;yj lbdthcbabwbhjdfnm gjhnatkm, xnj,s cybpbnm hbcr.
ß ghjnbd bcgjkmpjdfybz n.y. gjhnatkmyjq ntjhbb d rjyntrcnyjq htrkfvt,
rjnjhfz c ntjhbtq Ìfhrjdbxf yt bvttn ybxtuj j,otuj. Îlyfrj d ntjhbb
Ìfhrjdbxf tcnm ljdjkmyj ghbvtxfntkmysq gfhfljrc.
Äjgecnbv tcnm 2 nbgf wtyys[ ,evfu, ,evfuf Á zdyj [e;t À: vtymifz
lj[jlyjcnm b dsit hbcr. Â j,otv ckexft jgnbvfkmysq bydtcnbwbjyysq
gjhnatkm ,eltn cjlth;fnm j,t wtyyst ,evfub (tcntcndtyyj, ljkz ,evfub À
,eltn dsit). Ýnj ghjbc[jlbn, gjcrjkmre j,obq hbcr cyb;ftncz bp-pf
lbdthcbabrfwbb gjhnatkz.
Ïhbvthyj nfrjq ;t gfhfljrc ceotcndetn b ghb dpdtibdfybb. Åckb tcnm
ldt jwtyrb: jxtym [jhjifz À b jxtym gkj[fz Á, nj jgnbvfkmysq dtc Á yt
,eltn hfdty yek..
Ýnb ldf gfhfljrcf j,]zcyz.ncz jlyjq b njq ;t ajhvekjq. Òj;t ghjbc[jlbn xnj-nj dhjlt lbdthcbabrfwbb hbcrjd.
Êjyntrcnyfz htrkfvf
Âthytvcz r rjyntrcnyjq htrkfvt. Êfr z e;t ujdjhbk, gjrfpfntkm
rjydthcbb – jwtyrf rjydthcbb. Ò.t. vj;yj crfpfnm xnj dthjznyjcnm
rjydthcbb ghbvthyj hfdyf gjrfpfntk. rjydthcbb. Î,jpyfxbv gjrfpfntkm rfr
r, f dthjznyjcnm rfr p:
Òfr;t vs vj;tv crfpfnm, xnj dthjznyjcnm rjydthcbb ghbvthyj hfdyf gjrfpfntk. rjydthcbb cfqnf (m).
Èp xtuj gjkexftv dpdtityye. jwtyre:
Âtcf (w) gjl,bhf.ncz nfr, xnj,s cybpbnm gjuhtiyjcnm bnjujdjuj ghjuyjpf:
- dtc gjrfpfntkz rk.xf pfdbcbn jn xbckf rkbrjd. Åckb
xbckj rkbrjd yektdjt, nj jy hfdty yek. b ajhvekf cdjlbncz ghjcnj r
rjydthcbb cfqnf.
- dtc rjydthcbb cfqnf pfdbcbn jn njuj, yfcrjkmrj
hfpyfz rjydthcbz rk.xtds[ ckjd. ×tv ,jktt hfpyst rk.xtdst ckjdf, ntv
vtymit dtc m.
ÏÁÁ
Îlby bp vtnjljd htitybz yfitq pflfxb d vfncnfnbcnbrt – 'nj
,tnf-,byjvbfkmyfz vjltkm c jghtltktybtv fghbjhyjq lbcgthcbb gj vtnjle
yfb,jkmituj ghfdljgjlj,bz. Äkz rhfnrjcnb vs ,eltv tuj yfpsdfnm ÏÁÁ
(Ïhjcntqifz Átnf-Ábyjvbfkmyfz vjltkm).
Ýnj vtnjl bpdtcnty e;t ktn 50. Òfr;t jy egjvzyen d gfntynt Marin Software. Õjnz, djpvj;yj, d Marin Software ctqxfc bcgjkmpetn lheujq fkujhbnv.
Átnf-,byjvbfkmyfz vjltkm
Ñkexfqyst dtkbxbys
gjlxbyz.ncz ytrjnjhsv pfrjyfv hfcghtltktybzv. Çfrjy ujdjhbn j njv,
rfrbt pyfxtybz dcnhtxf.ncz xfot, f rfrbt – ht;t. Ífghbvth, k.ltq
chtlytuj hjcnf ,jkmit, xtv jxtym dscjrb[. Çyfz pfrjy, vs vj;tv cltkfnm
ytrjnjhst dsdjls. Ífghbvth, tckb vs djpmvtv ckexfqyjuj xtkjdtrf, nj c
dthjznyjcnm. d 95% tuj hjcn ,eltn yb;t lde[ vtnhjd.
Ó pfrjyf hfcghtltktybz tcnm 2 jcyjdys[ vjvtynf:
- Ìfnj;blfybt. Ãhe,j ujdjhz, chtlytt. Ífghbvth, chtlybq hjcn xtkjdtrf.
- Äbcgthcbz – ujdjhbn j njv, yfcrjkmrj hfpysq hjcn e hfpys[ k.ltq.
Èp ntjhbb dthjznyjcntq bpdtcnyj, xnj xbckj rjydthcbq gjlxbyztncz ,byjvbfkmyjve hfcghtltktyb. c gfhfvtnhfvb p (rjydthcbz) b n (xbckj rkbrjd). Ýnj pfgbcsdftncz nfr:
Åckb vs djpmvtv ckexfqysq rk.xtdbr c cfqnf (j rjnjhjv vs ,jkmit
ybxtuj yt pyftv), nj tuj rjydthcbz ,eltn gjlxbyznmcz ytrjnjhjve pfrjye.
Êfr yb nhelyj ljuflfnmcz, d ,tnf-,byjvbfkmyjq vjltkb cxbnftncz rjydthcbz
gjlxbyzncz ,tnf-hfcghtltktyb..
Ãlt m – vfnj;blfybt
(chtlyzz rjydthcbz e rk.xtdbrjd yf cfqnt). Ïfhfvtnh A – 'nj ytrjnjhfz
vthf «jlbyfrjdjcnb» rjydthcbb e rk.xtdbrjd. Îy j,hfnyj pfdbcbn jn
lbcgthcbb. ×tv ,jktt hfpyfz rjydthcbz e rk.xtq, ntv vtymit À.
Äjgecnbv, vs pyftv, xnj e rk.xtdbrf ,skj n rkbrjd b s rjydthcbq. Ècgjkmpez ntjhtve Áfqtcf, gjckt ljkub[ hfcxtnjd gjkexbv, xnj rjydthcbz 'njuj rk.xtdbrf bvttn cktle.ott hfcghtltktybt:
Ýnj yfit ghtlcnfdktybt j rjydthcbb rk.xtdbrf, cltkfyyjt yf jcyjdt tuj lfyys[ b hfcghtltktybz rk.xtdbrjd yf cfqnt.
Ìfnj;blfybt 'njuj hfcghtltktybz ,eltn hfdyj:
Ýnf ajhvekf ujdjhbn j chtlytq rjydthcbb rk.xtdjuj ckjdf, bvt.otuj s rjydthcbq b n rkbrjd. Ýnj bcrjvfz jwtyrf rjydthcbb.
Ïfhfvtnh À dsxbckztncz vtnjljv yfb,jkmituj ghfdljgjlj,bz. Íe;yj
gjlj,hfnm nfrjq À, rjnjhsq kexit dctuj cjjndtncndetn lfyysv cfqnf. Ýnjn
hfcxtn ljdjkmyj ckj;ty b lf;t yf rjvgm.ntht pfybvftn vyjuj dhtvtyb. Äkz
ytuj ye;yj dsxbckbnm gj 90 cgtwbfkmys[ vfntvfnbxtcrb[ aeyrwbq (ufvvf b
gjkbufvvf) yf rf;lsq rk.xtdbr.
Ñhtlytt dpdtityyjt
Ôjhvekf bp ghjikjq ukfds 'nj chtlytt dpdtityyjt gjrfpfntkz cfqnf b rk.xtdjuj ckjdf c dtcfvb:
×tv ,jktt jlyjhjlyst rk.xb yf cfqnt, ntv cbkmytt exbnsdftncz
gjrfpfntkm cfqnf. ×tv ,jkmit rkbrjd, ntv cbkmytt d ytq exbnsdftncz
gjrfpfntkm rk.xf. Ïhb 0 xbckt rkbrjd, yfif jwtyrf hfdyf m, f ghb
,tcrjytxyjv – r.
Ïhbvths
Äjgecnbv, e yfc tcnm m=1%, gjcvjnhbv, rfre. jwtyre vs lflbv.
Êkbrb
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Êjydthcbb
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Ïjrfpfntkm
|
A=1
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A=2
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A=3
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0
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0
|
ytn
|
1%
|
1%
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1%
|
1
|
0
|
0%
|
0.99%
|
0.995%
|
0.997%
|
1
|
1
|
100%
|
1.98%
|
1.49%
|
1.33%
|
10
|
0
|
0%
|
0.91%
|
0.95%
|
0.97%
|
10
|
1
|
10%
|
1.82%
|
1.43%
|
1.29%
|
10
|
10
|
100%
|
10%
|
5.7%
|
4.19%
|
100
|
0
|
0%
|
0.5%
|
0.66%
|
0.75%
|
100
|
1
|
1%
|
1%
|
1%
|
1%
|
100
|
2
|
2%
|
1.5%
|
1.33%
|
1.25%
|
100
|
10
|
10%
|
5.5%
|
4%
|
3.25%
|
1000
|
0
|
0%
|
0.09%
|
0.16%
|
0.23%
|
1000
|
10
|
1%
|
1%
|
1%
|
1%
|
1000
|
20
|
2%
|
1.9%
|
1.83%
|
1.77%
|
Êfr vs dblbv, yf ,jkmib[ lfyys[ jwtyrb yt cbkmyj jnkbxf.ncz jn gjrfpfntkz. Íj ghb vfks[ lfyys[ dpdtityyst jwtyrb fltrdfnytt gjrfpfntkz rjydthcbb.
Ïjuhtiyjcnm
Ìj;yj chfdybnm jib,rb gjrfpfntkz rjydthcbb b dpdtityyjq jwtyrb:
Ïhb vfkjv xbckt rkbrjd dpdtityyfz jwtyrf j,kflftn d ytcrjkmrj hfp
vtymitq gjuhtiyjcnm., yj c hjcnjv xbckf rkbrjd njxyjcnm j,jb[ jwtyjr
cnfyjdbncz ghbvthyj jlbyfrjdjq.
Ïhb,skm
Òjxyjcnm d idtqwfhcrbq ,fyr yt gjkj;bim, gj'njve cvjltkbhetv dkbzybt gjuhtiyjcnb yf ghb,skm:
100% vfrcbvfkmyfz ghb,skm (ghb bltfkmyjv ghjuyjpt). Êfr vs dblbv, ghb
bcgjkmpjdfybb dpdtityyjq jwtyrb ghb,skm dctulf dsit, xtv ghb
bcgjkmpjdfybb gjrfpfntkz rjydthcbb bkb dscnfdktybb jlbyfrjds[ cnfdjr.
MREM
Ýnj yt,jkmijt ekexitybt ÏÁÁ, 'njn fkujhbnv hf,jnftn d ,tcgkfnyjv jykfqy rfkmrekznjht rjydthcbb.
Ðfcxtn m
Îcyjdyfz ghj,ktvf ÏÁÁ d njv, xnj m ljk;yj ,snm jwtyrjq rjydthcbb
chtlytuj rk.xtdbrf, f yt jwtyrjq rjydthcbb gj cfqne. Ýnj hfpyst dtob,
gjcrjkmre e hfpys[ rk.xtds[ ckjd – hfpyjt xbckj rkbrjd.
Ífghbvth, e yfc tcnm 11 rk.xtds[ ckjd. Â 10 bp yb[ gj vbkkbjye
rkbrjd, b gjrfpfntkm rjydthcbb hfdty 2%, f d 11-jv 10 vbkkbjyjd rkbrjd b
gjrfpfntkm rjydthcbb hfdty 1%. Ïjrfpfntkm rjydthcbb cfqnf hfdty 1,5%,
yj rjydthcbz chtlytuj rk.xtdbrf d hfqjyt 1.9%.
Ýnf ghj,ktvf eceue,kztncz tot b ntv, xnj tcnm rjhhtkzwbz
vt;le xbckjv rkbrjd b rjydthcbtq. Ò.t. rjydthcbz pfdbcbn jn xfcnjnyjcnb
rk.xtdbrf. Íbprjxfcnjnybrb, j,sxyj bvt.n ,jkmie. rjydthcb.. Â cbke xtuj
m j,sxyj pfyb;ty.
Äf;t tckb rjhhtkzwbb bpyfxfkmyj ytn, nj jyf gjzdkztncz ghb fltrdfnyjq
hfccnfyjdrt cnfdjr, gjcrjkmre xbckj rkbrjd pfdbcbn jn cnfdrb, rjnjhfz d
cdj. jxthtlm pfdbcbn jn dthjznyjcnb rjydthcbb gj rk.xtdbre.
 bnjut, bp-pf 'njuj jwtyrf m vtnjljv ÏÁÁ j,kflftn ,jkmijq gjuhtiyjcnm., lf;t yf jxtym ,jkmib[ lfyys[,
lf;t ghb ,tcrjytxyjv xbckt rkbrjd b rk.xtds[ ckjd. Òfrbt jwtyrb d
cnfnbcnbrt yfpsdf.n ytcjcnjzntkmysvb. Òfrfz gjuhtiyjcnm d m ghbdjlbn r
njve, xnj njxyjcnm jwtyrb, jcj,tyyj, ybprjxfcnjnys[ rk.xtds[ ckjd
cyb;ftncz.
REM
×nj,s ekexibnm hfcxtn m, j,sxyj d vfncnfnbcnbrt bcgjkmpe.n
lde[gfhfvtnhbxtcre. vjltkm, rjulf vtnjljv yfb,jkmituj ghfdljgjlj,bz
botncz yt njkmrj À, yj tot b m. Îlyfrj nfrfz vjltkm ytcnf,bkmyf yf vfks[
lfyys[.
 rfxtcndt rjvghjvbccf vs bcgjkmpjdfkb REM (Random Effect Model) bp Ìtnf-fyfkbpf
(hfpltkf ntjhbb dthjznyjcntq). Â MREM m cxbnftncz gj ckj;yjq ajhvekt, d
rjnjhjq exbnsdftncz lbcgthcbz. Ýnj gjdsiftn njxyjcnm dsxbcktybz m b
cnf,bkbpbhetn hfcxtn yf vfks[ lfyys[.
Ïhb 100 rk.xtdbrf[:
Êfr vs dblbv, gjckt rfrjuj-nj gjhjuf xbckj rkbrjd yt ekexiftn jwtyre m
gj ÏÁÁ. Ýnj cdzpfyj c ntv, xnj rjhhtkzwbz vt;le rkbrfvb b rjydthcbtq
hj;lftn cbcntvfnbxtcre. jib,re.
Ïhb 1000 rk.xtdbrf[ 'njn 'aatrn tot pfvtnytt:
Êfr vs dblbv, gjuhtiyjcnm Marin gthtcnftn pfdbctnm jn j,]tvf lfyys[.
Ïjcrjkmre 'nf jib,rf d jcyjdyjv cdzpfyf yt c vfksv j,]tvjv lfyys[, f c
ghj,ktvfvb vjltkb.
Âtc m
Ïhb bcgjkmpjdfybb REM dtc m ntgthm pfdbcbn yt njkmrj jn A b m, yj tot
b xbckf rk.xtdbrjd yf cfqnt, xbckf rkbrjd e cfqnf, f nfr;t [fhfrnthf
hfcghtltktybz rkbrjd vt;le rk.xtdbrfvb.
Ífghbvth, tckb e yfc vfkj rkbrjd yf cfqnt, nj 'nj gjdsiftn jib,re d
dsxbcktybb m, b vs cyb;ftv dtc m. Åckb rkbrb hfcghtltktys ythfdyjvthyj,
yfghbvth, d jcyjdyjv yf[jlzncz e jlyjuj rk.xtdbrf, nj 'nj nj;t cyb;ftn
njxyjcnm m, b vs cyb;ftv dtc 'njq jwtyrb.
Ájktt njxysq ghjuyjp jib,rb gjdsiftn cnf,bkmyjcnm hfcxtnf À b njxyjcnm jwtyrb yf vfks[ lfyys[.
Äheubt ekexitybz
Êhjvt bcgjkmpjdfybz REM vjltkb tcnm tot cktle.obt ekexitybz ÏÁÁ.
Äbaathtywbfwbz
 rfxtcndt m kexit bcgjkmpjdfnm REM-jwtyre dpzne. yt gj dctv rk.xtdsv
ckjdfv, f gj dctv, rhjvt ntreotuj. Ákfujlfhz 'njve vs yt exbnsdftv
ldf;ls jlyb b nt ;t lfyyst. Òfr;t 'nj bp,fdkztn jn pfdsitybz jwtyrb À e
yt,jkmib[ rkbtynjd.
Îlyfrj lbaathtywbfwbz gjdsiftn dhtvz hfcxtnf dldjt. Îyf nht,etn
hfcxtnf 180 gjkbufvvf aeyrwbz yf 1 rk.xtdbr ghjnbd 90 d ckexft tt
jncencndbz.
Ìfrcbvev fgjcnthbjhb
À xnj tckb yf cfqnt jxtym vfkj rk.xtds[ ckjd? Â 'njv ckexft ghb dsxbcktybb À ,eltn ,jkmifz gjuhtiyjcnm.
Êfr b d ckexft rjydthcbb, ghb jwtyrt À vj;yj cltkfnm chtlytt
dpdtityysv lde[ jwtyjr: njuj À, rjnjhsq gjkexftncz vfrcbvevjv
ghfdljgjlj,bz, b njuj À, rjnjhsq d chtlytv yf,k.lftv e lheub[ rkbtynjd.
Äjgecnbv e rkbtynjd À d chtlytv hfdty 1,5. Åckb e rkbtynf djj,ot ytn lfyys[, nj vj;yj crfpfnm, xnj e ytuj À jrjkj 1,5.
 ntjhbb vs vj;tv lfnm ytgkj[e. jwtyre À, lf;t tckb e rkbtynf djj,ot
ytn lfyys[. Íf ghfrnbrt, tcntcndtyyj, yfv ye;ty tot b m, lkz dsxbcktybz
rjnjhjuj ye;ys [jnz-,s 10–30 rjydthcbq d cnfnbcnbrt pf ytcrjkmrj
vtczwtd.
 ,jktt ghjldbyens[ dthcbz[ ldb;rjd ghb jwtyrt À bcgjkmpetncz rhjvt
lfyys[ ntreotuj rkbtynf, hfcghtltktybt À e lheub[ rkbtynjd. Ýnj
yfpsdftncz vfrcbvevjv fgjcntjhb. Â bnjut yf yt,jkmib[ lfyys[ djphfcnftn
cnf,bkmyjcnm dsxbcktybq À, yf ,jkmib[ lfyys[ jwtyrb 'nbvb ldevz vtnjlfvb
gjxnb yt jnkbxf.ncz.
Ädf gthbjlf
 jgnbvbpfnjhf[ tcnm yfcnhjqrf gthbjl c,jhf cnfnbcnbrb. ×tv jy dsit
ntv ,jkmit e yfc lfyys[ b ntv vtymit gjuhtiyjcnm b dsit ghb,skm. Íf
gthdsq dpukzl 'njn gthbjl ye;yj edtkbxbnm.
Îlyfrj rjydthcbz rk.xtds[ ckjd vtyztncz dj dhtvtyb. Ýnj ghjbc[jlbn
bp-pf ctpjyyjcnb, gjujls, 'rjyjvbxtcrjq cbnefwbb, ekexitybq yf cfqnt,
htrkfvys[ frwbq b vyj;tcndf lheub[ afrnjhjd. ×tv jgthfnbdytt vs
htfubhetv yf 'nj, ntv ,jkmit ghb,skb gjkexbv. ×nj,s gjdscbnm
jgthfnbdyjcnm, ye;yj cjrhfnbnm gthbjl c,jhf cnfnbcnbrb.
Ïj'njve ye;yj bcrfnm rjvghjvbccye. lkbye gthbjlf. Åckb gthbjl ckbirjv
rjhjnrbq, nj njxyjcnm jwtyrb ,eltn ytdscjrjq. Ïhb ckbirjv lkbyyjv
gthbjlt, cbcntvf ,eltn htfubhjdfnm yf bpvtytybz c jxtym ,jkmijq
pflth;rjq.
 ytrjnjhs[ jgnbvbpfnjhf[ cnfdjr tcnm 2 gthbjlf. Ákfujlfhz jcyjdyjve
(,jktt lkbyyjve) vs gjkexftv vyjuj lfyys[, f ,kfujlfhz dcgjvjufntkmyjve
(,jktt rjhjnrjve) vs jgthfnbdyj htfubhetv yf bpvtytybz.
Äkz ,jkmib[ cfqnjd vj;yj dscnfdbnm dcgjvjufntkmysq gthbjl d ytcrjkmrj
ytltkm, f jcyjdyjq – d gjkujlf. Ákfujlfhz xtve ghjuyjp ,eltn
jlyjdhtvtyyj b njxysv, b jgthfnbdysv.
Èthfh[bz
Ìs ljdjkmyj kturj vj;tv cltkfnm Átnf-,byjvbfkmye. vjltkm bthfh[bxtcrjq. ×nj,s jyf exbnsdfkf lfyyst uheggs j,]zdktybq b rfvgfybb.
Ñyfxfkf vs jwtybdftv rjydthcb. rfvgfybb:
Ïjnjv dsxbckztv jwtyre rjydthcbb uheggs j,]zdktybz, bcgjkmpez dvtcnj m jwtyre rfvgfybb.
Ïjckt xtuj dsxbckztv jwtyre rk.xtdjuj ckjdf, bcgjkmpez jwtyre uheggs:
 rjytxyjv cxtnt, 'nb ajhveks cdjlzncz r chtlytdpdtifyjve 4-[ jwtyjr:
gj cfqne, rfvgfybb, uheggt b cfvjve rk.xtdbre. Ïhbxtv gjcrjkmre uhegg b
rfvgfybq yfvyjuj vtymit, xtv rk.xtds[ ckjd, nj htcehrjtvrjcnm hfcxtnf
ghfrnbxtcrb yt edtkbxbdftncz, tckb vs yt ,eltv bcgjkmpjdfnm
lbaathtywbfwb..
Îlyfrj bthfh[bxtcrfz vjltkm bvttn b cdjb ghj,ktvs:
- Êjydthcbz rfvgfybb b chtlyzz rjydthcbz rk.xtdjuj ckjdf rfvgfybb – 'nj hfpyst dtob. REM d hfvrf[ 'njq vjltkb yt htiftn ghj,ktve.
- Äjk;yf ,snm xtnrfz bthfh[bz. Ìs yt vj;tv exbnsdfnm rfrbt-nj lheubt jwtyrb dyt bthfh[bb, yfghbvth gj URL.
- Ðfcxtn A yf gjcktlyb[ ehjdyz[ cnfyjdbncz yt cnf,bkmysv e;t e chtlyb[ rkbtynjd.
×nj,s htibnm gjlj,yst ghj,ktvs nht,etncz ,jktt ckj;yfz vjltkm, rjnjhfz nht,etn e;t yfvyjuj ,jkmituj j,]tvf dsxbcktybq.
Ïjrfpfntkm jnrfpjd
 ntjhbb rhjvt ghjuyjpf gj uheggfv vs vj;tv bcgjkmpjdfnm b lheubt
jwtyrb. Ñfvfz df;yfz bp yb[ 'nj jwtyrf gj gjrfpfntk. jnrfpjd. Ífghbvth,
gecnm b – 'nj gjrfpfntkm jnrfpjd. ×tv dsit gjrfpfntkm jnrfpjd, ntv
vtymit rjydthcbz. Âjn cfvsq ghjcnjq vtnjl:
Ífghbvth, m = 1%, f gjrfpfntkm jnrfpjd gj cfqne hfdty 60%, njulf k = 1%/(1-60%)=1%/40%=0,025=2,5%.
Äjgecnbv, e rk.xtdbrf 80% jnrfpjd, njulf vs vj;tv lfnm cktle.oe. jwtyre rjydthcbb:
Äjgecnbv, e lheujuj rk.xtdbrf 30% jnrfpjd, njulf vs vj;tv lfnm cktle.oe. jwtyre rjydthcbb:
Ýne vjltkm vj;yj gjyznm ,kfujlfhz djhjyrt bp nht[ ifujd. Ñyfxfkf blen
rkbrb, xfcnm bp yb[ cnfyjdbncz jnrfpfvb. Îcnfdibtcz rkbrb (yt jnrfps) c
ytrjnjhjq dthjznyjcnm. (k) ghtdhfof.ncz d rjydthcbb.
×nj,s hfccxbnfnm dtc 'njq jwtyrb, ye;yj jwtybnm tt gjuhtiyjcnm. Îyf
cjcnjbn bp lde[ rjvgjytynjd. Ïecnm B 'nj dthjznyjcnm jnrfpf, njulf
- Ïjuhtiyjcnm
lfyys[. Âjpybrftn bp-pf njuj, xnj dthjznyjcnm jnrfpf yt hfdyf
gjrfpfntk. jnrfpjd. Ïhb edtkbxtybb xbckf rkbrjd cyb;ftncz dgkjnm lj yekz
yf ,tcrjytxyjv j,]tvt lfyys[. Î,sxyj d 5–20 hfp yb;t, xtv e gjrfpfntkz
rjydthcbq.
- Ñbcntvfnbxtcrfz gjuhtiyjcnm djpybrftn bp-pf njuj,
xnj yfif vjltkm yt f,cjk.nyj njxyf. Èp-pf njuj, xnj k e hfpys[ rk.xtds[
ckjd hfpyjt. Ýnf gjuhtiyjcnm yt pfdbcbn jn j,]tvf lfyys[. Ïhb
,tcrjytxyjv j,]tvt lfyys[ cevvfhyfz gjuhtiyjcnm ,skf ,s hfdyf
cbcntvfnbxtcrjq.
Ìj;yj bcgjkmpjdfnm ,jktt ckj;ye. vjltkm, d rjnjhjq tcnm tot b crhsnst jnrfps, d ytq cbcntvfnbxtcrfz gjuhtiyjcnm ytdtkbrf. Ýnf vjltkm jxtym njxyj ghtlcrfpsdftn ghjvt;enjxyst wtkb dhjlt lj,fdktybz njdfhf d rjhpbye.
Îib,rf lfyys[ nj;t ytdtkbrf. Î,sxyj dthjznyjcnm jnrfpjd d hfqjyt 50%,
f rjydthcbz 1%. Â 'njv ckexft, tckb ,s cbcntvfnbxtcrfz jib,rf ,skf
yektdjq, nj yfif ajhvekf ghb 10 rkbrf[ ,skf ,s nfrjq ;t njxyjq, rfr b
gjrfpfntkm rjydthcbb ghb 1000!
Åckb e rk.xtdjuj ckjdf ,eltn jxtym vfkj rkbrjd, nj jwtyrf gj jnrfpfv
,eltn [e;t jwtyrb gj uheggfv. Íj c hjcnjv xbckf rkbrjd jyf ,eltn ,scnhj
ekexifnmcz (yfvyjuj ,scnhtt, xtv gjrfpfntkm jnrfpjd) lj nt[ gjh, gjrf yt
ljcnbuytn cbcntvfnbxtcrjq jib,rb.
Î,sxyj jcyjdyfz vfccf rkbrjd e rkbtynf ghb[jlbncz rfr hfp yf nt
rk.xtdbrb, e rjnjhs[ yt cbkmyj vyjuj b yt cbkmyj vfkj rkbrjd. Ó nfrb[
rk.xtdbrjd kexit dctuj hf,jnftn jwtyrf gj jnrfpfv, b gj'njve jwtyrf gj
jnrfpfv pyfxbntkmyj gjdsiftn rfxtcndj bnjujdjq jwtyrb.
 j,otv, ytcvjnhz yf nj xnj jwtyrf gj jnrfpfv njkmrj jlyf bp vyjub[, tt drkfl d edtkbxtybt ghb,skb ljdjkmyj dscjr.
Êfr vs dblbv, ghb yt cbkmyj ,jkmijv xbckt rkbrjd, extn jnrfpjd pyfxbntkmyj gjdsiftn ghb,skm.
Çfrk.xtybt
Îgnbvbpfnjhs cnfdjr jwtybdf.n rjydthcb. gj vyj;tcnde afrnjhjd.
Ïjrfpfntkm rjydthcbb jlby bp yb[, yj ghb vfktymrjv xbckt rkbrjd e
rk.xtdbrf tuj drkfl d j,oe. jwtyre ,eltn ytpyfxbntkmysv.
Ïjrfpfntkm rjydthcbb j,sxyj buhftn ceotcndtyye. hjkm njkmrj e
dscjrjxfcnjnys[ rk.xtds[ ckjd, rjulf jy ljdjkmyj ljcnjdthyj jnhf;ftn
rjydthcb..
Ïhb hfcxtnt rjydthcbb bcgjkmpetncz chtlytt dpdtityyjt ytcrjkmrb[
jwtyjr. Åckb rfrfz-nj bp jwtyjr bvttn dscjre. gjuhtiyjcnm (rfr
gjrfpfntkm ghb vfkjv xbckt rkbrjd), nj jyf ghjcnj ,thtncz c jxtym
vfktymrbv dtcjv. Ýnj yt e[eliftn jwtyre.
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