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7/30/2019 Cursul 3 - Distributiile variabilelor aleatoare
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Dgstrgoutgglb virgioglblar ilbitairb
Eursul 5
7/30/2019 Cursul 3 - Distributiile variabilelor aleatoare
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Zbhtru a papulitgb dbnghgti, ngbeirbg virgiolb ilbitairb gg bstb
isaegiti a dgstrgoutgb eirb dbnghbstb praoioglgtitbi db ipirgtgb i
ngbeirbg vilarg pasgoglb i iebstbg virgioglb &diei bxgsti uh hu`ir nghgt`isuriogl db virgioglb' siu taitb sbturglb pasgoglb db vilarg pasgoglb&diei virgioglblb suht dbnghgtb pb da`bhgul rbil'(
A virgioli bstb a eirietbrgstgei aosbrviti siu `isuriti( A virgiolidgh papulitgi studgiti paitb ng ilbitairb siu eahstihti(
Aosbrvitgb; virgiogli bstb `irg`bi eirb virgizi db li uh ghdgvgd liiltul(
Eb bstb a virgiogli ilbitairb1
7/30/2019 Cursul 3 - Distributiile variabilelor aleatoare
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A dgstrgouȓgb i praoioglgtitglar bstb uh `adbl `itb`itge eirb bxprg`ilbmituri dghtrb vilairbi virgioglbg sg praoioglgtitbi bg db ipirgȓgb èhpapuliȓgb(
Dgstrgoutgi praoioglgtitglar
Dgstrgoutgb dgserbti Dgstrgoutgb eahtghui
7/30/2019 Cursul 3 - Distributiile variabilelor aleatoare
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Dgstrgoutgi praoioglgtitglar
x
x p x p 9'& sg 9'&:
Dgstrgouȓgi dgserbtą bstb bstb nar`iti dgh oirb i eirar ghiltg`b bstbprapartgahili eu praoioglgtitbi( Zraoioglgtitbi virgioglbg ilbitairb V dbi lui vilairbi xg bstb;
gg x p x x Z
Dgstrgouȓgi eahtghuą bstb a euroą hbtbdą, eu irgi db suo euroi bmiląeu praoioglgtitbi, istnbl èheït praoioglgtitbi ei x si sb inlb èh ghtbrvilul&i, o' bstb;
dx x n o xi Z o
i
Ub i`ghtbstb ei;
&9'
&?'
7/30/2019 Cursul 3 - Distributiile variabilelor aleatoare
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@bdgi i uhbg dgstrgouȓgg db praoioglgtitg bstb a `ąsurą itbhdghȓbg ebhtrilb i dgstrgouȓgbg( @bdgi sb dbnghbstb istnbl;
9g
dgserbtix,
eahtghuix,
gg x p x
dx x xn
Zbhtru a virgiogli ilbitairb dgserbti eu H vilarg sg p&xg' 0 9!H,beuitgi &5' sb rbdueb li;
&5'
H
x H
g
g 9
Dgstrgoutgi praoioglgtitglar
7/30/2019 Cursul 3 - Distributiile variabilelor aleatoare
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Dgspbrsgi ?
bxprg`i g`prąȗtgbrbi, rąspïhdgrbi siuvirgioglgtitbi uhbg dgstrgouȓgg3 bstb db dbnghgti istnbl;
9g
?
?
?
dgserbtix,
eahtghuix,
gg x p x
dx x n x
Zbhtru a virgiogli ilbitairb dgserbtą eu eu H vilarg sg p&xg' 0 9!H,beuitgi &4' sb rbdueb li;
&4'
H
x H
g
9g
?
?
Gh prietgei sb utglgzbizi ioitbrbi stihdird;
H
x H
g
9g
?
?
Dgstrgoutgi praoioglgtitglar
7/30/2019 Cursul 3 - Distributiile variabilelor aleatoare
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Dgstrgoutgg dgserbtb - dgstrgoutgglb nrbevbhtblar rblitgvb pbhtru bxpbrg`bhtb`isurioglb(
_ispuhsurg di - hu(
• Dgstrgoutgi Obrhaullg• Dgstrgoutgi ogha`gili
• Dgstrgoutgi ogha`gil - hbmitgvi
• Dgstrgoutgi Zagssah
• Dgstrgoutgi fgpbrmba`btrgei
• Dgstrgoutgi ̀ ultgha`gili
Uu`i rispuhsurglar ObrhaullgHu`irul db ghebreirgpbhtru il clbi bvbhg`bht
Zuhetb ghtr-uh spitgu dit
Hu`irul db kudbeitg ghightbiprg`ulug sueebs
_bzultitb `ultgplb pasgolb pbhtru ngbeirbghebreirb(
Dgstrgoutgg dgserbtb g`partihtb
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Dgstrgoutgi ogha`gili
Rh praebs eahstą dghtr -a sbevbhȓą db h ghebreirg ghdbpbhdbhtb sggdbhtgeb(
Ghebreirb ghdbpbhdbhti - rbzultitul ngbeąrug ghebreirg hu dbpghdb dbrbzultitblb ghebreirglar ihtbrgairb(
_bzultitul ngbeąrbg ghebreirg bstb ngb uh sueebs, ngb uh bȗbe(
Diei praoioglgtitbi sueebsulug, p bstb eahstihtą pbhtru argeb praebs,ituheg hu`ąrul db sueebsb x dgh h ghebreirg irb dgstrgouȓgiogha`gilą eu piri`btrgg h sg p, dbnghgtg istnbl(
xh x
p p xh x
h
x Z
'9&')&)
)
'&Zraoioglgtitbi;
@bdgi;hp
Ioitbrbi stihdird;'9& ph
&2'
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Dgstrgouȓgi ogha`gilą
Dgstrgouȓgi ogha`gilą sb utglgzbizi nrbevbht èh ghmghbrgi dbeilgtitb(
Bstb `adblul db praoioglgtitb earbspuhzątar pbhtru prblbvirbidb praob db li a papuliȓgb ghnghgti uhdb;
p bstb nrieȓguhbi db pradusb dbnbetb siu hbeahnar`b dghpapuliȓgb(
x bstb hu`ąrul db irtgealb hbeahnar`b dghtr -uh bȗihtgahilbitargu db h blb`bhtb(
Db bxb`plu, dieą p 0 :,9: ȗg h 0 92, ituheg praoioglgtitbi db iaoȓghb uh pradus hbeahnar` x sb eileulbizą eu nuhetgiogha`dgst dgh Bxebl(
7/30/2019 Cursul 3 - Distributiile variabilelor aleatoare
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Nar`i nuhetgglar db praoioglgtitb ogha`gili
Aosbrvitgb; Eu eit erbstb h sg p sb iprapgb db :,2, dgstrgoutgi sbiprapgb db nar`i sg`btrgei i dgstrgoutgbg har`ilb(
7/30/2019 Cursul 3 - Distributiile variabilelor aleatoare
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Bxpbrg`bht; Ub iruhei 2 `ahbdb(Bvbhg`bhtul db ghtbrbs; eitb `ahbdb eid pb pirtbi eip(
Zbhtru a `ahbdi, praoilgtitbi ei si ipiri eipul &uh sueebs' bstbp 0 :(2( Hu`irul db eipbtb eirb ipir li iruheirbi i 2 `ahbdb
bstb a virgioli ogha`gili ilbitairb eu h 0 2 sg p 0 :(2(
hr( db eipbtb Aosbrvit Tbarbtge
: 9 9(2>9 99 =(69? 99 92(>55 97 92(>54 > =(692 ? 9(2>
Bxpbrg`bhtul sb rbpbti db 2: db arg(
: 9 ? 5 4 2
?:969>949?
9:6>4?
:
Bxb`plb db dgstrgoutgb ogha`gili
7/30/2019 Cursul 3 - Distributiile variabilelor aleatoare
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_bzultit Nrbevbhti Nrbevbhti rblitgvi? ? :(:4
5 4 :(:64 4 :(:62 5 :(:>> 4 :(:6= = :(946 7 :(967 5 :(:>
9: 2 :(9:99 = :(949? ? :(:4tatil 2: 9(::
Daui zirurg sb iruhei sg sb ghsu`bizi ghdgeitgglb lar &virgioliilbitairb x'( Bxpbrg`bhtul sb rbpbti db 2: db arg(
Z&x 6' 0
Z&x >' 0
Z&4 x 9:' 0
55!2: 0:(>>
5=!2: 0 :(=4
54!2: 0 :(>6
Bxpbrg`bhtul eu daui zirurg
Zraoioglgtitgglb virgioglbg
ilbitairb x;
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A dgstrgouȓgb dgserbtą utglą èh eahtralul stitgstge il eilgtąȓgg bstb dgstrgouȓgiZagssah( A virgiogli ilbitairb irb dgstrgoutgb Zagssah eu piri`btrul ,diei nuhetgi db praoioglgtitb bstb;
b0?(=96…
Dgstrgoutgi Zagssah
b x
x p x
)'&
Rh nbha`bh ilbitargu eirb ipirb &hu`irulug db dbnbetb' pb uhgtitbi dbsupriniȓą, db valu`, db tg`p, bte, bstb ipraxg`it eu dgstrgouȓgi Zagssah(
Bx(; Hu`ąrul db dbnbetb eb ipir èhtr -uh dgspazgtgv sb`geahduetar sbdgstrgougb Zagssah eu 0 4( Zraoioglgtitbi ei uh dgspazgtgv sb`geahduetar sblbetit ilbitargu si eahȓghi dauą siu `ig puȓghb dbnbetb bstb;
0
? 0
Zraoioglgtitbi;
@bdgi;Dgspbrsgi;
pbhtru 8 :
Ub eileulbizi eu nuhetgi ZAGUUAH dgh Bxebl
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Dgstrgoutgi Zagssah
Dgstrgoutgi praoioglgtitgg Zagssah pbhtru dgnbrgtb vilarg ilb piri`btrulug (
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Dgstrgoutgi fgpbrmba`btrgei
Ghtr-a papuliȓgb nghgtą nar`iti dgh H blb`bhtb, eitbvi dgh iebstbblb`bhtb sb èheidrbizą èhtr -a elisą db ghtbrbs, D&D≤H'(
Rh bȗihtgah ilbitargu db h blb`bhtb eu x blb`bhtb sb èheidrbizą èh elisi db ghtbrbs( x ipirtghb uhbg dgstrgouȓgg db praoioglgtitbfgpbrmba`btrgeb diei;
D'`gh&h,(((,:,9,?,((((x
h
H
xh
D H
x
D
x p
@bdgi;
Zraoioglgtitb;
Dgspbrsgi;
H
hD
9
9?
H
h H
H
D
H
hD
))
)
oio
i
o
i
Ug`oal pbhtru ea`oghitgg
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Dgstrgoutgi fgpbrmba`btrgei
Dgstrgoutgi fgpbrmba`btrgeą bstb `adblul db praoioglgtitbearbspuhzątar sblbetirgg uhug bȗihtgah ilbitargu db h aogbetb,nąrą èhlaeugrb, dghtr -a `ulȓg`b db H blb`bhtb dgh eirb D suhthbeahnar`b siu eu dbnbetb(
Èh iebstb iplgeiȓgg, x rbprbzghtą hu`ąrul db irtgealb hbeahnar`bdgh bȗihtgah(
Db bx(; sb prbsupuhb eą a `ulȓg`b eahȓghb 9:: db irtgealb,dghtrb eirb 2 hu suht eahnar`b eu ebrghtblb( Diei 9: irtgealb
suht sblbetitb li èhtï`plirb, nąrą èhlaeugrb, eirb bstbpraoioglgtitbi db i mąsg uhul siu `ig puȓghb blb`bhtbhbeahnar`b èh bȗihtgah1
Ub utglgzbizi nuhetgi FWZMBA@DGUT dgh Bxebl
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Dgstrgoutgi Ziseil ȗg dgstrgouȓgg èhrudgtb
Dgstrgouȓgglb Ziseil, li nbl ei dgstrgouȓgi ogha`gilą, sboizbizi pb ghebreirbi lug Obrhaullg(
Ub g-iu èh eahsgdbrirb a sueebsguhb db ghebreirgghdbpbhdbhtb, ngbeirb eu praoioglgtitbi db sueebs p ȗg sbhatbizą eu x ghebreirbi gh eirb sueebsul ipirb il r lbi( x
bstb a virgioglą ilbitairb eu dgstrgouȓgb Ziseil dbpraoioglgtąȓg dbnghgti istnbl;
r x9
9
9
r xr p p
r
x x p
p
r
?
? 9
p
pr
Zraoioglgtitb;
@bdgb;
Dgspbrsgb;
&2'
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Dgstrgoutgi Ziseil ȗg dgstrgouȓgg èhrudgtb
Dauą eizurg spbegilb ilb dgstrgouȓgbg Ziseil sb iplgei gh EUE
Diei r 8 : Dgstrgouȓgi sb hu`bȗtb dgstrgouȓgi ogha`gilą hbmitgvą( Beuiȓgi &2'
bstb dgstrgouȓgb ogha`gilą hbmitgvą pbhtru r ghtrbm(Dgstrgouȓgi ogha`gilą hbmitgvą bstb utgli pbhtru tgpurg dgnbrgtb db ditb
/hu`ąrioglb/, eu` ir ng ipirgȓgi hbeahnar`gtąȓglar pb uhgtitb dbpradus(
Èh dgstrgouȓgi ogha`gilą, sb stioglbstb `ąrg`bi bȗihtgahulug ȗg sbaosbrvi hu`ąrul db sueebsb(
Gh dgstrgouȓgi ogha`gilą hbmitgvą, sb stioglbstb hu`ąrul db sueebsb
ȗg sb dbtbr`ghi dg`bhsguhbi bȗihtgahulug( Iebst eahebpt driplgei èh dgnbrgtb tgpurg db praolb`b db bȗihtgahirb( Dieą r 0 9
dgstrgouȓgi bstb mba`btrgeą, idgei dgstrgouȓgi hu`ąrulug db ghebreirgObrhaullg pïhą li prg`ul sueebs(
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• Dgstrgoutgi har`ili
• Dgstrgoutgi Lam Har`il
• Dgstrgoutgi Mi``i
• Dgstrgoutgi ?
• Dgstrgoutgi N• Dgstrgoutgi t
• Dgstrgoutgi ]bgoull• Dgstrgoutgi ̂ ilarglar bxtrb`b
&TGp G sg tgp GG'
Ub utglgzbizi pbhtru tbstblbstitgstgeb(
A `irb pirtb i stitgstgeggghnbrbhȓgilb sb nuhdi`bhtbizipb iebisti dgstrgoutgb
^irgiolblb dgh `bdgul i`ogbhtil
Duriti pïhą li bȗbe,
Dgstrgouȓgg ilb duritbg db vgiȓą
Dgstrgoutgg eahtghub
^irgioglb ilbitairb eahtghub sb dbnghbse pbhtru hu`brb eu
vilarg eahtghub gh da`bhgul rbil( Zraoioglgtąȓglb sb eileulbizi
pbhtru taitb sbturglb db hu`brb pasgoglb(
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Dgstrgoutgi har`ili
Dgstrgouȓgb har`ilą bstb ebi `ig g`partihti dgstrgouȓgb, itït èhtbargb eit ȗg gh iplgeitgglb stitgstgegg(Dieą x bstb a virgioglą ilbitairb har`ilą, ituheg dgstrgouȓgi db
praoioglgtitb i lug x bstb;
x- ?
9?
2,:
x
b x n
@bdgi dgstrgoutgbg
har`ilb bstb &- < < #' sg dgspbrsgi bstb? 8 :(
7/30/2019 Cursul 3 - Distributiile variabilelor aleatoare
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>6" dgh irgi tatilibstb ghtrb - sg #(
>6(:'& V Z
Dgstrgoutgb sg`btrgei dbnghgti pb ghtbrvilul &-, # ' i eirbg nar`i bstbdbnghgti db dag piri`btrg, `bdgi, , eirb bstb ebhtrul dgstrgoutgbg, sgioitbrbi stihdird, , eirb dbtbr`ghi g`pristgbrbi dgstrgoutgbg(
Irgi0(>6
Dgstrgoutgi har`ili
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• Nuhetgi db dbhsgtitb bstb gh nar`i db elapat, sg`btrgei(• >6" dgh irgi db suo euroą bstb èhtrb (
• 72" dgh irgi db suo euroą bstb èhtrb ?(
• 77(=" dgh irgi db suo euroą bstb èhtrb 5(
(>6
(72
??
Zraprgbtitglb dgstrgouȓgbg har`ilb
_bmuli b`pgrgei
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Dgstrgoutgi har`ili
Dgstrgouȓgi eu`ulitgvą har`ilą bstb dbnghgtą ei praoioglgtitbi virgioglbgilbitairb har`ilą x ≤ i;
?
9?
2,:
i x
dxbi N i x Z
Ghtbmrili hu paitb ng bviluiti èh nar`ą èhefgsą( Ub utglgzbizisefg`oirbi db virgioglą;
x
[
Bviluirbi sb nieb ghdbpbhdbht db ȗg ?
;
ii z Z i x Z
&' bstb nuheȓgi db rbpirtgȓgb eu`ulitgvą i dgstrgouȓgbg har`ilb stihdird
eu 0 : sg ? 0 9(
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Taitb virgioglblbilbitairb har`ilb pat ngearblitb eu virgioglbilbitairb har`ilbstihdird(
A virgiogląilbitairb har`iląstihdird irb`bdgi : ȗg dbvgiȓgi
stihdird 9(
Dgstrgoutgi har`ili stihdird
5 5??
: #9 #? #5-9-?-5
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Db eb bstb g`partihti dgstrgoutgi stihdirdgziti1 Zbhtru eą praoioglgtitbi argeirug bvbhg`bht il uhbg
virgioglb ilbitairb har`ilb eu ioitbrbi stihdird ȗg
`bdgi ditb paitb ng eileuliti dgh tioblblb dgstrgouȓgbghar`ilb stihdird(
Dgstrgoutgi har`ili stihdird
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_^Dgst-?>
Tiobl dgstrgoutgbg har`ilb
stihdirdgziti
[:(: 9(:
Tioblul 9 dą zahblb ląsitb db z(
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Tbarb`i lg`gtą ebhtrilą
Dgstrgouȓgb har`ilą sb prbsupuhb ei bstb `adblul db praoioglgtitbidbevit pbhtru a virgioglą ilbitairb( Iebisti gpatbzi trbougbvbrgngeiti(
Tbarb`i lg`gti ebhtrili;
Dieą x9, x?,( ( ( , xh suht virgioglb ilbitairb ghdbpbhdbhtb eu `bdgi ȗg dgspbrsgi ? ȗg dieą y 0 x9 # x? #( ( ( # xh, ituheg dgstrgouȓgi;
h
g
g
h
g
g y
9
?
9
sb iprapgb dgstrgouȓgi H&:, 9' diei h sb iprapgb db ghnghgt(
_bzulti eą su`i i h virgioglb ilbitairb dgstrgougtb ghdbpbhdbht bstb
ipraxg`itgv har`ilą, ghdgnbrbht db dgstrgouȓgglb virgioglblar ghdgvgduilb(
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Dgstrgouȓgi lam-har`ilą
Diei virgioglblb sb earblbizi prghtr-a rbliȓgb bxpahbhȓgilą, x 0 bxp&w' sg bxpahbhtul w bstb a virgioglą ilbitairb, ituheg sg x bstb avirgioglą ilbitairb(
Diei w sb dgstrgouȓgb har`il, dgstrgouȓgi lug x sb hu`bstb dgstrgouȓgb lam-har`ilą( Hu`blb rbzultą dgh trihsnar`irbi lh &x' 0 w(
Nuheȓgi db dgstrgouȓgb eu`ulitgvą pbhtru x bstb;
ii z Z iw Z iw Z i x Z i N
lhlhlhbxp
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Ngb w a dgstrgouȓgb har`ilą eu `bdgi ȗg dgspbrsgi ?, ituheg
x 0 bxp &w' bstb a virgioglą ilbitairb eu dgstrgoutgi lam-har`ilą(
Nuhetgi dgstrgoutgbg lam-har`ilą bstb;
x:
?
lhbxp
?
9?
?
x
x x n
?
bxp
?
9???? bb
@bdgi;
Dgspbrsgi;
Dgstrgouȓgi lam-har`ilą
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Tb`i db eisi
Iltb tgpurg db dgstrgoutgg eahtghub
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^irgiogli [
Ub stihdirdgzbizi vilarglb prgh bxprg`irbi iebstari èh nuhetgb dbioitbrbi stihdird
Ub `ąsairą dgstihȓi db li `bdgb &èh eizul èh eirb `bdgi bstbikustitą li :' li virgiogli;
s
x x [ g
g
Zrbzbhtirbi ditblar gh nar`i stihdird pbr`gtb ei ditblb si sbea`pirb eu ditblb iltar dgstrgoutgg@bdgi bstb bmili eu zbra
Ioitbrbi stihdird bstb bmili eu uhu^ilarglb nuhetgbg db dgstrgoutgb stihdirdgzitb sb gi dgh tioblb(
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Zraolb`i; Ghiltg`bi a`ulug dgh Hbihdbrtfil Zapuliȓgi sefblbtblar Hbihdbrtfil Ghiltg`bi `isuriti pirb są ur`bzb a dgstrgouȓgb har`ilą…
x 0 9>5(= e`
s 0 2(=7 e`
Ghtrboirbi 9; Eb prapartgb i papulitgbg irb ghiltg`bi 89>2 e`1
[ 0 1[ 0 &9>2 -9>5(='!2(=7 0 :(?5
Nalasghd Tioblul E-?nde&:(?5' 0 :(4:7:2
_ispuhs 4:(7"
^irgiogli [
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(466:5 (464:2 (46::> (4=>:6
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nde dn&x' 0 :(76 Ub nalasbstb Tioblul E-93 eiuti :,76 rbzulti [ 0 ?(:2
Ub eileulbizi x dgh nar`uli lug [;
x 0 ?(:2 ½ 2(=7 # 9>5(= 0 9=2(> e`
x [ x gg
Ghtrboirbi ?; Eirb bstb ghiltg`bi gh eirb sb gheidrbizi 76" dgh papuliȓgb1
_ispuhs; F 0 9=2,> e`(
^irgiogli [
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Dgstrgouȓgi `bdgbg bȗihtgahulug
hu sb ȗtgb nar`i dgstrgouȓgbg papuliȓgbg3 sb prbsupuhb ei bstb a dgstrgoutgb har`ili
Ub utglgzbizi praprgbtąȓglb dgstrgouȓgbg har`ilb Ub vgzuilgzbizi dgstrgoutgi `bdgglar uhug hu`ąr `irb db
bȗihtgaihb…
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db aogebg dgspuhb` db uhul dghtrb iebstb bȗihtgaihb ((( hu putb` ȗtg uhdb sb pazgtgahbizi `bdgi bsihtgahulug èh ripart eu
`bdgi papuliȓgbg, dir putb` bstg`i uh ghtbrvil gh eirb ir putbi ng ((( iebst lueru dbpghdb db
`irg`bi bsihtgahulug a bstg`irb i dgspbrsgbg papuliȓgbg
Eu eit bȗihtgahul bstb `ig `ge ȗg papuliȓgi `ig dgspbrsiti, eu ititpraoioglgitbi ei ̀ bdgi bȗihtgahul si ngb `ig dbpirtb db `bdgi
papuliȓgbg bstb `ig `irb( Iebsti ingr`itgb sb rbnlbetą èh beuiȓgi utglgzitą pbhtru eileulul dgspbrsgbg`bdgbg bȗihtgaihblar;
h s x
??
Dgstrgouȓgi `bdgbg bȗihtgahulug
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Dgstrgoutgi `bdgglar earbspuhzitairb sbturglar ilbitairb db bsihtgaihb luitb dghtr-a papulitgb tghdb sprb dgstrgoutgi har`ili(
Eahnar`gtitbi eu a dgstrgouȓgi har`ilą erbȗtb eu
dg`bhsguhbi bȗihtgaihblar(
@bdgglb sb dgstrgougb èh kurul vilargg `bdgg i papuliȓgbg
x V
Tbarb`i lg`gtbg ebhtrilb
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Ioitbrbi stihdird i `bdgglar bsihtgaihblar bstb brairbi stihdird i `bdgbg bstg`itb;
hhh sb 9
?
Zb oizi uhug bȗihtgah, sb eileulbizi, eu a ihu`gti praoioglgtitb, uhghtbrvil eirb eahȓghb `bdgi papuliȓgbg utglgzihd brairbi stihdird;
h [ x
uhdb [ 0 9(7> pbhtru praoioglgtitbi :(72
Dgstrgouȓgi `bdgbg bȗihtgahulug
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Bxb`plu
virnurg db simbiti h 0 2:
luhmg`bi `bdgb x 0 ??(> ``
s 0 4(? ``
Brairbi stihdird 0 11
??(> ¹ 9(7>½4,?½&2:'-:,2
??(> ¹ 9(9> `` Eu praoioglgtitbi db 72" `bdgi papuliȓgbg sb inli èh ghtbrvilul
?9(4 - ?5(6
274(:2:
?(4
h
s
h s [ x
Dgstrgouȓgi `bdgbg bȗihtgahulug
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Ghtbrvil db gherbdbrb
Ghtbrvilblb db gherbdbrb suht bxprg`itb gh tbr`bhgg praoioglgtitggoizitb pb primul db sb`hgngeitgb (
Rh ghtbrvil db gherbdbrb &9- ', bxprg`i niptul ei praoioglgtitbi eipiri`btrul papulitgbg si sb misbisei gh ghtbrvilul db gherbdbrbbstb 9- , gir praoioglgtitbi ei piri`btrul papulitgbg si sbmisbisei gh iniri ghtbrvilulug db gherbdbrb bstb (
Ebl `ig dbs nalasgtb suht lg`gtblb db gherbdbrb &primul dbsb`hgngeitgb' db 72", eirb ghdgei niptul ei praoioglgtitbi ei
vilairbi `bdgbg hbeuhaseuti dgh papulitgb si sb inlb ghtrbiebstb lg`gtb bstb db 72", gir gh iniri lar bstb db 2"(
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Ghtbrvil db gherbdbrb - prim db sb`hgngeitgb
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Lg`gtblb db gherbdbrb ilb `bdgbg papulitgbg &²' dbnghbse ghtbrvilul dbgherbdbrb pbhtru `bdgi papulitgbg pb oizi `bdgbg bsihtgahulug sgbstg`irbi dgspbrsgbg papulitgbg(
Zbhtru bsihtgaihblb eu h 8 5: lg`gtblb db gherbdbrb sb oizbizi pbripartul ergtge earbspuhzitar praoioglgtitgg isaegitb(
Zbhtru bsihtgaihb eu h < 5: lg`gtblb db gherbdbrb sb oizbizi pbvilarglb lug t dgh tioblb, earbspuhzitairb hu`irulug db mridb dblgobrtitb sg praoioglgtitgg isaegitb(
Lg`gtblb db gherbdbrb ilb vilargg `bdgg
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Dgstrgoutgi t
Dgstrgoutgi `bdgglar bsihtgaihblar `geg &rbdusb hu`brge' hu bstb
tatdbiuhi har`il dgstrgougti, efgir diei papulitgi dgh eirb dbrgvibstb har`il dgstrgougti(
Zrgh bsihtgah `ge sb èhtblbmb iebl bsihtgah eu h < 5:(
Diei papulitgi bstb dgstrgougti har`il, dgstrgoutgi bsihtgaihblar ur`bizi dgstrgoutgi t, dgstrgoutgb eirb rbnlbeti a `ig `irb virgitgbditariti sihsbg gh ea`piritgb eu dgstrgoutgi har`ili(
Bstb eahtghui, sg`btrgei, uhg`adili, virgizi db li ― li # , bstb `ult
`ig lirmi gh ea`piritgb eu dgstrgoutgi har`ili(
Diei bsihtgaihblb erbse, dgstrgoutgi t sb iprapgb db dgstrgoutgi har`ili,gir pbhtru uh hu`ir ghnghgt db mridb db lgobrtitb eblb ? dgstrgoutgg suhtgdbhtgeb sg vilarglb ergtgeb ilb lug t suht bmilb eu ripartul ergtge ildgstrgoutgbg har`ilb
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Dgstrgoutgi t bstb sg`btrgei, li nbl ei a dgstrgoutgb har`ili, dir dbvghbtat `ig pliti aditi eu `gesarirbi da`bhsguhgg bsihtgahulug
Dgstrgoutgi t
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Dgstrgouȓgi `bdgbg bȗihtgahulug pbhtru bsihtgaihb `geg
Zbhtru i eileuli ghtbrvilul db èherbdbrb earbspuhzitar `bdgbg uhar bsihtgaihb eu hu`ir `ge db `isuritarg &har`il siu ipraipbhar`il dgstrgougtb' sb utglgzbizi a nar`uli `adgngeiti;
t sb aotghb dgh tioblul praoioglgtitglar pbhtru dgstrgoutgi t siunalasghd pramrihul BVEBL(
h
t x
Èh tioblul dgstrgoutgbg t, vilarglb suht mrupitb èh nuhetgb db primul dbsb`hgngeitgb db mridblb db lgobrtitb ― dn 0 h -9(
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