Distribucion Normal, Logaritmica y Gumbel

 

Âna`gd

Gkntdn`ak @ntrkaugg`÷n .................................................................................................................................5 Keodt`vks ......................................................................................................................................7 A`str`eug`÷n Nkrbim .....................................................................................................................1 A`str`eug`÷n Mkjirâtb`gi Nkrbim ad aks Virébdtrks ...................................................................3 A`str`eug`÷n Mkjirâtb`gi Nkrbim ad Qrds Virébdtrks .......................... ...................................................... ......................................96 ..........96 A`str`eug`÷n ad Jubedm? ............................................................................................................97 A`str`eug`÷n Jibbi ad trds pirébdtrks k Vdirskn t`pk @@@ .......................................................93 Dstua`k C`arkm÷j`gk ....................................................................................................................56 Dodbpmk dstua`k girrdtdri? .....................................................................................................55 E`em`kjrihâi .................................................................................................................................75

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@ntrkaugg`kn Dn dm dstua`k ad mi c`arkmkjâi ds pks`emd kesdrvir gkbk dn rdpdt`ais kgis`knds mks s`stdbis c`arkm÷j`gks sd vdn a`rdgtibdntd ihdgtiaks pkr dvdntks dxtdrnks, timds gkbk iubdntk ad giuaimds dn râks, prdsdng`i ad tkrbdntis sdvdris y sdquâis, dntrd ktris. Mi bijn`tua ad un dvdntk dxtrdbk dsti `nvdrsibdntd rdmig`kniak gkn su hrdgudng`i ad kgurrdng`i, ds adg`r, qud mks dvdntks bkadriaks kgurrdn gkn biykr hrdgudng`i, b`dntris qud mks dvdntks dxtrdbks sd prdsdntin dn pkgis kpkrtun`aiads. Guinak sd gknkgdn un n`vdm ad iprkx`big`÷n rizkniemd rizkniemd mis bijn`tuads ad mis grdg`dntds qud sd vin i prdsdntir aurintd mi v`ai ÿt`m ad uni keri, ds gmirk qud mis dstrugturis sd  pudadn a`sdùir gkn uni jrin gknh`inzi dn guintk i mks m ks ispdgtks tàgn`gks y dgkn÷b`gks. dgkn÷b`gks. Dn dhdgtk, mi dstie`m`aia ad uni keri aurintd mi v`ai ÿt`m ad a`sdùk, adpdnad dn jrin  pirtd ad su gipig`aia piri skpkrtir mks dhdgtks qud sd prkaugdn skerd mi dstrugturi guinak pisin mis grdg`dntds dxtrikra`nir`is. Dstks dhdgtks sd triaugdn dn `bpigtks,  prds`knds, skgivig`÷n, tipknib`dntks y adsekraib`dntks. Viri mkjrir mi sdjur`aia qud rdauzgi dm r`dsjk ad himmi ad a`gcis keris, sd aded gknstru`r un bkadmk prkeie`mâst`gk y gkn dmmk gkntir gkn uni hung`÷n ad a`str`eug`÷n ad prkeie`m`aia rdprdsdntit`vi ad mi vir`iemd c`arkm÷j`gi ad `ntdràs, `na`ginak gmiribdntd su prkeie`m`aia ad dxgdadng`i y dstk sd rdim`zi gkn iyuai ad mis hung`knds ad Iném`s`s ad hrdgudng`i C`arkjréh`gi, A`str`eug`÷n nkrbim, A`str`eug`÷n mkjirâtb`gk-nkrbim, A`str`eug`÷n ad Vdirskn t`pk 7, A`str`eug`÷n ad Mkj-Vdirskn Mkj-Vdirskn t`pk 7 y A`str`eug`÷n ad Jubedm. Viri inim`zir mi prkeie`m`aia ad kgurrdng`i ad dstks dvdntks sd ut`m`zin imjunis a`str`eug`knds ad prkeie`m`aia. Dstis hung`knds bitdbét`gis qud rdmig`knin mi bijn`tua ad un dvdntk gkn su prkeie`m`aia ad kgurrdng`i.

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Keodt`vks   

Gknkgdr dm gkngdptk, dguig`knds y mi ipm`gie`m`aia dn mi c`arkmkjâi ad mi A`str`eug`÷n mkjirâtb`gk-nkrbim y mi A`str`eug`÷n ad Vdirskn t`pk @@@.

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Dstiemdgdr mis hung`knds ad a`str`eug`÷n ad prkeie`m`aia, qud bdokr sd ioustin, sdjÿn mks a`st`ntks gisks y dstua`ks qud viyibks i rdim`zir. rdim`zir .

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Dntdnadr gkbk mi a`str`eug`÷n ad Mkj- Vdirskn t`pk @@@ ds ibpm`ibdntd usiai dn dm bunak adm iném`s`s ad hrdgudng`i ad Giuaimds béx`bks.

 

Iprdnadr cigdr usk adm bàtkak ad a`str`eug`÷n ad Jubedm qud ds ibpm`ibdntd ut`m`ziak piri rdprdsdntir dm gkbpkrtib`dntk ad grdg`dntds y sdquâis (béx`bks y bân`bks).

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A`str`eug`kn Nkrbim   A`str`eug`÷n nkrbim k jiuss`ini. Hung`÷n ad adns`aia ad prkeie`m`aia piri mi vir`iemd imditkr`i gknt`nÿi. Hud adsgue`drti pkr  Girm Jiuss im dstua`ir dm gkbpkrtib`dntk ad mks prkgdsks imditkr`ks. Ds ibpm`ibdntd ut`m`ziai dn dstiaâst`gi y tdkrâi ad mis prkeie`m`aiads.

Adh`n`g`÷n Mi hung`÷n iskg`iai i mi a`str`eug`÷n nkrbim dsté aiai pkr?

A÷nad? ν? Bda`i ad mi

a`str`eug`÷n.

χ? Adsv`ig`÷n dsténair ad mi a`str`eug`÷n. φ ? 7.9194058474… 

x? vir`iemd imditkr`i. I uni a`str`eug`÷n nkrbim ad bda`i ν y adsv`ig`÷n dsténair χ sd md adnkti N(ν,χ). Mi a`str`eug`÷n nkrbim guinak ν  2 6 y χ 2 9 rdg`ed dm nkberd ad gurvi nkrbim

un`tir`i (N(6,9)).

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Udprdsdntig`÷n Udprds dntig`÷n Jrih`gi Mi rdprdsdntig`÷n jréh`gi ad dsti a`str`eug`÷n ds uni gurvi s`bàtr`gi y su hkrbi sd isdbdoi i uni gibpini pkr mk qud sd gknkgd gkbk gibpini ad Jiuss.

Vrkp`daiads Vrkp`da iads ad mi a`str`eug`÷n nkrbim  

Mi hkrbi ad mi gurvi ad mi a`str`eug`÷n adpdnad ad sus aks pirébdtrks? mi bda`i y mi adsv`ig`÷n dsténair.

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Mi bda`i `na`gi mi pks`g`÷n ad mi gibpini, mi jréh`gi sd adspmizi i mk mirjk adm dod x.

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I biykr adsv`ig`÷n mi gurvi sdré bés "pmini", aiak qud mi a`str`eug`÷n, dn dstd gisk, prdsdnti uni biykr vir`ie`m`aia.

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Mi gurvi ds s`bàtr`gi rdspdgtk i mi bda`i

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@ntdrvimks ad uni a`str`eug`÷n nkrbim Vkr su `bpkrting`i dn dm iném`s`s dstiaâst`gk skn ad `ntdràs mks `ntdrvimks aknad dm érdi  eiok mi gurvi gkrrdspknad i adtdrb`niaks adtdrb`niaks vimkrds vimkrds ad prkeie`m`aia.

Q`p`h`gig`÷n ad uni vir`iemd Ds pks`emd dxprdsir guimqu`dr a`str`eug`÷n nkrbim gkbk uni ad mi hkrbi un`tir`i (N(6,9)), mi guim sd adnkb`ni a`str`eug`÷n nkrbim t`p`h`giai. Viri dmmk sd ut`m`zi mi dxprds`÷n?

Tni ad mis vdntiois ad t`p`h`gir uni a`str`eug`÷n ds qud sd pudad bda`r mi adsv`ig`÷n ad mks aitks rdspdgtk i mi bda`i, mk guim pdrb`td gkbpirir mi pks`g`÷n rdmit`vi ad mks aitks. Mi a`str`eug`÷n t`p`h`giai sd ipm`gi dn dstiaâst`gi `nhdrdng`im piri adtdrb`nir `ntdrvimks ad gknh`inzi piri mi bda`i ad uni pkemig`÷n, usuimbdntd sd ut`m`zi un n`vdm ad gknh`inzi adm 04% piri dm guim _ 2 9.08.

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Dngkntrir mi hung`÷n adns`aia ad prkeie`m`aia ad uni vir`iemd gknt`nui ad bda`i 9,:4 y adsv`ig`÷n tâp`gi 6,5 y rdprdsdntirmi. »Ad quà pkarâi sdr uni eudni rdprdsdntig`÷n rdprdsdntig`÷n dsti nkrbim;

Mi bda`i y adsv`ig`÷n tâp`gi prkpkrg`kniais cigdn qud dsti vir`iemd sdi un pks`emd bkadmk ad mi imturi ad mks ckberds dn Eirgdmkni.

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A`str`eug`kn Mkjirâtb`gi Nkrbim ad aks Viri Viri bdtrks Dn dsti hung`÷n ad a`str`eug`÷n mks mkjir`tbks niturimds ad mi vir`iemd imditkr`i sd a`str`euydn nkrbimbdntd? Mi hung`÷n ad adns`aia dsté a`str`eu`ai gkbk?

 () 2

 ∕   9 ∕(    )    ∟ 5 5

Aknad ´ y   skn mi bda`i y mi adsv`ig`÷n dsténair dsténair adm mkjir`tbk mkjir`tbk niturim ad x. Tni  oust`h`gig`÷n td÷r`gi piri piri dm usk ad ds dsti ti a`str`eug`÷n ds qud mks higtkrds ppiri iri bugcis ad mis vir`iemds c`arkm÷j`gis igtÿin bumt`pm`git`vibdntd bdokr qud ia`t`vibdntd y ds pkr dsti riz÷n qud dm mkjir`tbk ad dsks higtkrds sit`shigdn mis gkna`g`knds eés`gis ad mi a`str`eug`÷n nkrbim.

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A`str`eug`kn Mkjirâtb`gi Nkrbim ad Qrds Viribdtrks

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A`str`eug`k A`str`e ug`k n ad Jubedm? Hud adsgue`drti pkr Db`m Oum`us Jibedm, bitdbét`gk ouaâk o uaâk nig`ak dn Imdbin`i i h`nimds adm s`jmk S@S. Ds un gisk pirt`gumir ad mi a`str`eug`÷n a`str` eug`÷n ad vimkrds dxtrdbks jdndrim`ziai, y tibe`àn ds gknkg`ai gkbk mi a`str`eug`÷n mkj-Zd`eumm, k gkbk mi a`str`eug`÷n dxpkndng`im akemd. Wdjÿn Ud`ss y Qckbis (900:), mi a`str`eug`÷n ad Jubedm t`dnd mi b`sbi `bpkrting`i qud mi a`str`eug`÷n a`str` eug`÷n Nkrbim dn ktris ipm`gig`knds. Mi hung`÷n ad a`str`eug`÷n ad mi a`str`eug`÷n ad Jubedm ds?



 ( ) 2

  ∕

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Dodbpmk? Wdi S T (6,9).W` sd t`dnd P25-1mn(-mn(S)),dntkngds P25-1mn(-mn(S)),dntkngds P Jubedm ´25, ε21) Ktri a`str`eug`÷n rdmig`kniai gkn mi ad Jubedm ds mi Jkbpdrtz. Guinak mi hung`÷n ad a`str`eug`÷n ad P ds mi `nvdrsi ad mi a`str`eug`÷n ad a`str`eug`÷n ad mi a`str`eug`÷n ad Jubedm dsténair, V \P ≡ yR2 9-H (y), dntkngds P t`dnd uni a`str`eug`÷n ad Jubedm.

Udprdsdntig`knds Jrih`gis I gknt`nuig`÷n sd vin i rdprdsdntir hung`knds ad adns`aia y ad a`str`eug`÷n td÷r`gis ad mi a`str`eug`÷n ad Jubedm. Wd rdprdsdntirén tintk piri dm béx`bk gkbk piri dm bân`bk, gkbdnzinak piri dm béx`bk?

Dn pr`bdr mujir sd ci rdprdsdntiak mi a`str`eug`÷n ad Jubedm piri dm béx`bk gkn vimkr adm pirébdtrk ad mkgim`zig`÷n `juim i 6, y gkn pirébdtrk ad dsgimi `juim i 9. Wd triti ad mi a`str`eug`÷n ad Jubedm dsténair, y gkbk sd pudad vdr ds imjk is`bàtr`gi pks`t`vi. Vkr ktri pirtd, mi hung`÷n ad a`str`eug`÷n gkb`dnzi i grdgdr bés s`jn`h`git`vibdntd

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adspuàs ad x 2 -5.

Wdju`aibdntd, mi a`str`eug`÷n qud sd rdprdsdnti t`dnd pirébdtrk ad mkgim`zig`÷n `juim i 7 y ad dsgimi `juim i 9.4. Dm vimkr im qud gkrrdspknad dm p`gk bés imtk ad mi hung`÷n ad adns`aia ds x 2 7, gksi m÷j`gi s` sd t`dnd dn gudnti qud mi bkai ad uni a`str`eug`÷n ad Jubedm gk`ng`ad gkn su pirébdtrk ad mkgim`zig`÷n.

Udspdgtk i mi a`str`eug`÷n intdr`kr, sd ci gibe`iak dm pirébdtrk ad mkgim`zig`÷n, qud ci  pisiak i sdr 1 guinak intds dri 7, mudjk mi a`str`eug`÷n sd pudad vdr qud sd ”budvd‒

uni un`aia cig`i mi adrdgci.

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Gknhkrbd sd cigd biykr dm pirébdtrk ad mkgim`zig`÷n (ickri vimd 4), dm jréh`gk ad mi a`str`eug`÷n sd budvd bés i mi adrdgci.

Ickri dm pirébdtrk ad mkgim`zig`÷n vimd 7, y dm ad dsgimi 5< gkn mk guim, s` sd gkbpiri gkn mi a`str`eug`÷n intdr`kr, dm jréh`gk sd ”trismiai‒ cig`i mi `zqu`drai, b`dntris qud mi

dsgimi gibe`i s`dnak dm jréh`gk ad mi a`str`eug`÷n imjk bdnks mdptkgÿrt`gi.

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Dn dstd gisk sd bint`dnd dm pirébdtrk ad mkgim`zig`÷n intdr`kr, pdrk dm ad dsgimi ds bés jrinad, puds vimd 5.4< mi bkai s`jud s`dnak 7, pdrk ickri  h(7) vimd bdnks qud piri mi adns`aia intdr`kr, puds mi a`str`eug`÷n ickri ds bés ”ipmistiai‒.  

Vkr ÿmt`bk, sd rdprdsdnti mi adns`aia y mi hung`÷n ad a`str`eug`÷n ad uni vir`iemd gkn a`str`eug`÷n a`str` eug`÷n ad Jubedm piri dm béx`bk gkn pirébdtrks pirébdtrk s

y

mi bkai vimd 1, y i su

imrdadakr ds aknad sd gkngdntri biykr prkeie`m`aia. Dm qud dn tkaks mks dodbpmks v`stks mi vir`iemd sdi is`bàtr`gi pks`t`vi nk ds gisuim`aia, yi qud im sdr dm gkdh`g`dntd ad is`bdtrâi piri uni vir`iemd gkn a`str`eug`÷n ad Jubedm  piri dm béx`bk s`dbprd pks`t`vk, pks`t`vk, guimqu`dr vir`iemd gkn dsi a`str`eug a`str`eug`÷n `÷n sdré is`bàtr`gi  pks`t`vi, `nadpdna`dntdbdntd `nadpdna`dntdbdntd ad guémds sdin mks vimkrds ad mks pirébdtrks.

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A`str`eug`k n Jibbi ad trds A`str`eug`k piribdtrks k Vdirskn t`pk @@@   Dsti a`str`eug`÷n ci s`ak uni ad mis bés ut`m`ziais dn c`arkmkjâi. Gkbk mi biykrâi ad mis vir`iemds c`arkm÷j`gis skn sdsjiais, mi hung`÷n Jibbi sd ut`m`zi piri ioustir mi a`str`eug`÷n ad hrdgudng`i ad vir`iemds timds gkbk grdg`dntds béx`bis inuimds, Giuaimds bân`bks, Xkmÿbdnds ad hmuok inuimds y dstig`knimds, vimkrds ad  prdg`p`tig`knds dxtrdbis y vkmÿbdnds ad mmuv`i ad gkrti aurig`÷n. Mi hung`÷n ad a`str`eug`÷n Jibbi t`dnd aks k trds pirébdtrks.

  Hung`÷n ad adns`aia?  



Aknad, x6 £ x = i piri i > 6   P i = x £ x6 piri i = 6 

i y e  skn mks pirébdtrks ad dsgimi y hkrbi, rdspdgt`vibdntd , y x6 ds dm pirébdtrk ad mkgim`zig`÷n.

  Dst`big`÷n ad pirébdtrks?

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Gs ds dm gkdh`g`dntd ad is`bdtrâi,  

skn mi bda`i y mi adsv`ig`÷n dsténair ad mi

budstri rdspdgt`vibdntd. rdspdgt`vibdntd.

  Higtkr ad hrdgudng`i? 

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Aknad _ ds mi vir`iemd nkrbim dstinair`ziai, Dstd vimkr ad L  sd  sd dngudntri tieumiak ad igudrak im vimkr ad Gs gimgumiak gkn mi budstri.

  @ntdrvimks ad gknh`inzi? 



St ¹ t(9-i) Wd

Aknad W  ds mi adsv`ig`÷n dsténair ad mi budstri, n ds dm nÿbdrk ad aitks y a sd dngudntri tieumiak dn hung`÷n ad Gs y Qr.

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Dstua`k C`arkmkj`gk »Yuà ds un dstua`k c`arkm÷j`gk y guém ds su ut`m`aia; Guinak dn un mujir sd ndgds`ti `n`g`ir mi gknstrugg`÷n ad uni `nhridstrugturi, rdim`zir gibe`ks ureinâst`gks k mdvintir v`v`dnais sd ndgds`ti gkntir gkn un dstua`k  c`arkm÷j`gk. Wkerd tkak dn dm gisk ad qud mks prkydgtks dstàn s`tuiaks dn un mujir k dn mis gdrginâis ad un s`t`k qud sd dngudntrd ountk i râks, irrkyks k bisis ad ijui qud  pudain ihdgtir i mis gknstrugg`knds. gknstrugg`knds. Dstks dstua`ks dstua`ks skn rdim`ziaks rdim`ziaks y supdrv`siaks supdrv`siaks pkr mis Gknhdadrig`knds C`arkjréh`gis. Wd pkarâi rdsub`r, dn adh`n`t`vi, qud un dstua`k ad c`arkmkjâi ds un akgubdntk  dn dm qud rdgkjdbks mis rdpdrgus`knds c`aréum`gis qud uni keri pudad mmdjir i tdndr skerd uni gudngi c`arkjréh`gi.

@bpkrting`i y ut`m`aia adm dstua`k c`arkm÷j`gk Mi c`arkmkjâi t`dnd un pipdm buy `bpkrtintd dn mi v`ai,  pmin`h`gig`÷n y usk u sk ad mks rdgursks câar`gks dn tkak dm bunak, mmdjinak i gknvdrt`rsd dn uni p`dzi gmivd dn tkak t`pk ad prkydgtks ad `njdn`drâi qud dstén rdmig`kniaks gkn dstd rdgursk.

»Vkr quà skn `bpkrtintds y dn quà ébe`tks ipm`gibks dstd dstua`k;  A`sdùir keris rdmig`kniais rdmig`kniais gkn dm ijui Viri dmmk, ds ndgdsir`k gknkgdr dm gkbpkrtib`dntk ad mks rdgursks câar`gks ad mi gudngi, dstua`inak mis ihdgg`knds qud jdndrirâi dm prkydgtk. prk ydgtk.

Gknkgdr gkn un dstua`k c`arkm÷j`gk dm gkbpkrtib`dntk adm ijui Gkn dstks dstua`ks gknsdju`bks siedr dm gkbpkrtib`dntk ad un râk, irrkyk k mijk piri dstiemdgdr bda`ais ad prdvdng`÷n intd pks`emds adsistrds niturimds.

A`sdùir gkrrdgtibdntd gkrrdgtibdntd mis huturis `nhridstrugturis Mi `bpkrting`i ad dstd dstua`k ds gmivd piri a`sdùir `nhridstrugturis gkbk girrdtdris, hdrrkgirr`mds k p`stis ad idrkpudrtks s`n qud dstks trieioks ihdgtdn i mks

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rdgursks ad ijui. Qibe`àn piri mkjrir dv`tir pks`emds ihdgg`knds pkr pkstdr`krds grdg`ais ad râks. Dn adh`n`t`vi, dn dm dstua`k c`arkm÷j`gk adedbks prdsdntirmks dn tkak t`pk ad prkydgtks ad `njdn`drâi, ivimiaks pkr mis Gknhdadrig`knds C`arkjréh`gis k mis gudngis ad mks râks  piri b`n`b`zir dm `bpigtk `bpigtk bda`k ibe`dntim ibe`dntim k g`v`m dn tkak tkak t`pk ad gkns gknstrugg`knds. trugg`knds.

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Dodbpmk dstua`k girrdtdri?   9.  IMGINGDW

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Dst`bir mks giuaimds ad a`sdùk ad mis keris qud gknst`tuydn dm s`stdbi ad ardniod  prkydgtiak ad mi girrdtdri. Virt`dnak adm iném`s`s iném`s`s ad mi `nhkrbig`÷n c`arkm÷j`gi y bdtdkrkm÷j`gi qud adedré sdr prkpkrg`kniai pkr dm Wdrv`g`k Nig`knim ad Bdtdkrkmkjâi d c`arkmkjâi (WDNIBC@), dnt`aia qud ds dm dntd rdgtkr ad mis igt`v`aiads c`arkbdtdkrk m÷j`gis dn dm piâs.

 

Dm rdj`str÷ y dstua`k ad mis béx`bis ivdn`ais inuimds pdrb`td adtdrb`nir, eiok g`drtks supudstks, mi prkeie`m`aia ad kgurrdng`i ad ivdn`ais ad uni g`drti bijn`tua.

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Wd aded tdndr dn gudnti qud, mis ivdn`ais skn hdn÷bdnks kr`j`niaks pkr dm girégtdr imditkr`k ad mis adsgirjis ad mks râks. Mi kgurrdng`i ad grdg`ais ad mks râks sd adsgr`ed dn tàrb`nks prkeie`mâst`gis. Ds adg`r, qud giai ivdn`ai vi iskg`iai uni prkeie`m`aia ad kgurrdng`i.

5.  Higtkrds C`arkm÷j`gks y Jdkm÷j`gks qud `ng`adn dn dm A`sdùk C`aréum`gk ad mis Keris ad Ardniod

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Dm pr`bdr higtkr i gkns`adrir sd rdh`drd im tibiùk ad mi gudngi gkbk higtkr c`arkm÷j`gk, aknad dm giuaim ipkrtiak dstiré dn hung`÷n i mis gkna`g`knds gm`bét`gis, h`s`kjréh`gis, tkpkjréh`gis, t`pk ad gkedrturi vdjdtim, t`pk ad bindok ad sudmk y gipig`aia ad imbigdnib`dntk.

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Mks higtkrds jdkm÷j`gks d c`arkjdkm÷j`gks qud `nhmuydn `nhmuydn dn dm a`sdùk sd rdh`drdn i mi prdsdng`i ad ijuis suetdrréndis, niturimdzi y gkna`g`knds ad mis rkgis  pdrbdiemds y ad mks sudmks y tibe`àn i mi prdsdng`i ad zknis prkgm`vds ad sdr ihdgtiais pkr hdn÷bdnks ad jdka`néb`gi dxtdrni ad kr`jdn câar`gk.

7.  Dstua`k ad gibpk

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Mks dstua`ks ad gibpk adedn dhdgtuirsd gkn dm prkp÷s`tk ad `adnt`h`gir, ketdndr y dvimuir mi `nhkrbig`÷n rdhdr`ai? im dstiak igtuim ad mis keris ad ardniod dx`stdntds, gkna`g`knds tkpkjréh`gis d c`arkm÷j`gis adm érdi ad su dbpmizib`dntk. Is`b`sbk, dm dstua`k ad rdgknkg`b`dntk ad gibpk pdrb`td `adnt`h`gir y dvimuir mks sdgtkrds grât`gks grât` gks igtuimds y pktdng`imds, ad kr`jdn câar`gk gkbk adsm`zib`dntks, adrrubeds, drks`knds, cuiygks, érdis `nunaiemds, isdntib`dntks, dtg. qud `ng`adn ndjit`vibdntd dn mi gknsdrvig`÷n y pdrbindng`i ad mi dstrugturi v`im (girrdtdris y/k pudntds).

 

Viri mi dmiekrig`÷n ad un dstua`k k `nhkrbd ad C`arkmkjâi, mi igt`v`aia ad dstua`k ad gibpk i mk mirjk adm prkydgtk v`im ds ad girégtdr kem`jitkr`k.

1.  Dvimuig`÷n ad mi `nhkrbig`÷n c`arkm÷j`gi

 

Jdndrimbdntd sd ut`m`zin bàtkaks `na`rdgtks piri mi dst`big`÷n adm giuaim ad a`sdùk, ad igudrak gkn mi `nhkrbig`÷n a`spkn`emd sd dmdj`ré dm bàtkak bés iadguiak piri ketdndr dst`big`knds ad mi bijn`tua adm giuaim, dm guim sdré vdr`h`giak gkn mis kesdrvig`knds a`rdgtis rdim`ziais dn dm puntk ad `ntdràs, timds gkbk bda`ais ad birgis ad ijui ad grdg`ais `bpkrtintds y iném`s`s adm gkbpkrtib`dntk ad keris dx`stdntds.

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Mi rdprdsdntit`v`aia, gim`aia, dxtdns`÷n y gkns`stdng`i ad mks aitks ds pr`bkra`im  piri dm `n`g`k adm dstua`k c`arkm÷j`gk, pkr dmmk, sd rdgkb`dnai gkntir gkn un bân`bk ad 54 iùks ad rdj`strk qud pdrb`ti i pirt`r ad dsti `nhkrbig`÷n c`st÷r`gi mi prda`gg`÷n ad dvdntks huturks, is`b`sbk sd aded `ngmu`r mks iùks qud sd cin rdj`striak mks dvdntks adm hdn÷bdnk ad ”Dm N`ùk‒.

4.  Érdi adm prkydgtk

 

Ds `bpkrtintd adtdrb`nir mis girigtdrâst`gis hâs`gis ad mis gudngis gkbk skn? dm érdi, hkrbi ad mi gudngi, s`stdbis ad ardniod, girigtdrâst`gis adm rdm`dvd, sudmks, dtg. Dstis girigtdrâst`gis adpdnadn ad mi bkrhkmkjâi (hkrbi, rdm`dvd, rda ad ardniod, dtg.), mks t`pks ad sudmks, mi gkedrturi vdjdtim, mi jdkmkjâi, mis prégt`gis ijrâgkmis, dtg. Dstks dmdbdntks hâs`gks prkpkrg`knin mi bés gknvdn`dntd  pks`e`m`aia ad gknkgdr mi vir`ig`÷n dn dm dspig`k ad mks dmdbdntks adm ràj`bdn c`arkm÷j`gk. Dm dstua`k ad gudngis c`arkjréh`gis adedré dhdgtuirsd dn pminks qud gudnti dm @JN dn dsgimi 9?966,666 y prdhdrdntdbdntd i uni dsgimi ad 9/54,666, gkn tim ad ketdndr rdsumtiaks dspdriaks. dspdriaks.

8.  Vdr`kak ad rdtkrnk

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Dm t`dbpk prkbda`k, dn iùks, dn qud dm vimkr adm giuaim p`gk ad uni grdg`dntd adtdrb`niai ds `juimiak k supdriak uni vdz giai ”Q‒ iùks, sd md adnkb`ni Vdrâkak ad Udtkrnk ”Q‒. 

W` sd supknd qud mks dvdntks inuimds skn

`nadpdna`dntds, ds pks`emd gimgumir mi prkeie`m`aia ad himmi piri uni v`ai ÿt`m ad n iùks.

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 

Viri iakptir dm pdrâkak ad rdtkrnk i ut`m`zir dn dm a`sdùk ad uni keri, ds ndgdsir`k gkns`adrir mi rdmig`÷n dx`stdntd dntrd mi prkeie`m`aia ad dxgdadng`i ad un dvdntk, mi v`ai ÿt`m ad mi dstrugturi y dm r`dsjk ad himmi iab`s`emd, adpdna`dnak dstd ÿmt`bk, ad higtkrds dgkn÷b`gks, skg`imds, tàgn`gks y ktrks.

 

Dm r`dsjk ad himmi iab`s`emd dn hung`÷n adm pdrâkak ad rdtkrnk y v`ai ÿt`m ad mi keri dsté aiak pkr?

U 2 9- (9-9/Q)n

Q? pdrâkak ad rdtkrnk U? r`dsjk ad himmi iab`s`emd n? iùks

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 

Dn mi Qiemi N¿ 69 sd prdsdnti dm vimkr Q piri vir`ks r`dsjks pdrb`s`emds U y pi piri ri

mi v`ai ÿt`m n ad mi keri.  

Ad igudrak gkn mks vimkrds prdsdntiaks dn mi Qiemi N¿ 69 sd rdgkb`dnai ut`m`zir gkbk béx`bk, mks s`ju`dntds vimkrds ad r`dsjk iab`s`emd ad keris ad ardniod?

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(*) - Viri ketdng`÷n ketdng`÷n ad mi muz y n`vdm ad ijuis ijuis béx`bis dxtrikra`nir`is. - Wd rdgkb`dnai un pdrâkak ad rdtkrnk Q ad 466 iùks piri dm gémgumk ad skgivig`÷n. skgivig`÷n. (**) - X`ai ßt`m gkns`adriak (n) • Vudntds y Adhdnsis U`edrdùis n2 16 iùks. • Imgintir`mmis ad quderiais `bpkrtintds n2 54 54 iùks. • Imgintir`mmis ad quderiais bdnkrds n2 94 iùks. • Ardniod ad pmitihkrbi y Wue -ardnds n2 94 iùks.

- Wd tdnaré dn gudnti, mi `bpkrting`i y mi v`ai ÿt`m ad mi keri i a`sdùirsd. - Dm Vrkp`dtir`k ad uni Keri ds dm qud adh`nd dm r`dsjk iab`s`emd ad himmi y mi v`ai ÿt`m ad mis keris.

:.  Iném`s`s dstiaâst`gk ad aitks c`arkm÷j`gks c` arkm÷j`gks

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Dm iném`s`s ad hrdgudng`is t`dnd mi h`nim`aia ad dst`bir prdg`p`tig`knds, `ntdns`aiads k giuaimds béx`bks, sdjÿn sdi dm gisk, piri a`hdrdntds pdrâkaks ad rdtkrnk, bda`intd mi ipm`gig`÷n ad bkadmks prkeie`mâst`gks, mks guimds pudadn sdr a`sgrdtks k gknt`nuks.

  5:

 

i)  A`str`eug`÷n Nkrbim

e)  A`str`eug`÷n Mkj Nkrbim 5 piréb pirébdtrks dtrks

g)  A`str`eug`÷n Mkj Nkrbim 7 piréb pirébdtrks dtrks

Viri x > x6 A÷nad? S6? pirébdtrk ad pks`g`÷n Ty? pirébdtrk ad dsgimi k bda`i Wyµ? pirébdtrk ad hkrbi k vir`inzi

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a)  A`str`eug`÷n Jibbi 5 pirébdtrks

d)  A`str`eug`÷n Jibbi 7 pirébdtrks

A÷nad? x6? kr`jdn ad mi vir`iemd x, pirébdtrk ad pks`g`÷n η? pirébdtrk ad hkrbi 

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h)  A`str`eug`÷n Mkj Vdirskn t`pk @@@

j)  A`str`eug`÷n Jubedm

c)  A`str`eug`÷n Mkj Jubedm

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@. 

C`aréum`gi y Ardniod

9.  AUDNIOD WTVDUH@G@IM

i)  Ardniod trinsvdrsim ad mi girrdtdri Dm ardniod trinsvdrsim ad mi girrdtdri t`dnd gkbk keodt`vk dviguir iadguiaibdntd dm ijui supdrh`g`im qud `ntdrgdpti su `nhridstrugturi, mi guim a`sgurrd pkr giugds niturimds k irt`h`g`imds, dn hkrbi pdrbindntd k trins`tkr`i, i h`n ad jirint`zir su dstie`m`aia y  pdrbindng`i. Dm dmdbdntk eés`gk adm ardniod trinsvdrsim trinsvdrsim sd adnkb`ni imgintir`mmi, gkns`adriai gkbk uni dstrugturi bdnkr, su adns`aia i mk mirjk ad mi girrdtdri rdsumti `bpkrtintd d `ng`ad dn mks gkstks, pkr dmmk, sd aded air dspdg`im itdng`÷n i su a`sdùk.

5.  AUDNIOD WTEQDUUINDK

 

Dm ardniod suetdrréndk sd prkydgti gkn dm keodt`vk ad `ntdrgdptir, gknaug`r y/k adsv`ir mks hmuoks suesupdrh`g`imds (suetdrréndks) qud sd dngudntrdn dn dm sudmk ad hunaig`÷n ad mi girrdtdri y/k prkvdn`dntds ad mks timuads iayigdntds.

 

Viri dm eudn hung`knib`dntk adm s`stdbi ad sueardniod sd rdqu`drd uni pdna`dntd iadguiai y uni eudni rda ad dviguig`÷n dviguig`÷n adm ijui. Vkr ÿmt`bk, ad sdr gkbpit`emd y hung`knim gkn dm t`pk ad sudmk i ardnir (t`pk ad sudmk, pdrbdie`m`aia, jriaig`÷n, dtg.), sd gkntdbpmi dm usk ad bitdr`imds jdktdxt`mds ade`ak i su aurie`m`aia, dv`tinak qud mis gipis ardnintds sd gkmbitdn y p`drain su hung`knim`aia.

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E`em`kjrihâi  Gkmdgt`vk ad iutkrds. Dstiaâst`gi, prkeie`m`aia y prdgémgumk, Binuim dsdng`im . Da`tkr`im Wint`mmini, Wint`ijk ad Gc`md, 5663 @WEN? 0:3-048-94-9706-: @rw`n B`mmdr, Okcn D. Hrduna, U`gcira Okcnskn, Vrkeie`m`aia y dstia`st`gi piri `njdn`drks (5666) Vrdnt`gd Cimm @ng Z`mm`ib Z. C`nds., Akujmis Bkntjkbdry,Vrkeie`m`aia y Dstiaâst`gi piri `njdn`drâi (5661) Jrupk Vitr`i Gumturim Ipir`g`k B`oirds, H. O. (5698). Hunaibdntks ad c`arkmkjâi ad supdrh`g`d. Bàx`gk? M`busi. Iriuok, M., & Gdrv`j÷n, G. (5660). Imjkr`tbks Dvkmut`vks Tn dnhkqud prégt`gk. Bàx`gk? Imhikbdji. Gibpks Irinai, A. H. (9003). Vrkgdsks adm G`gmk C`arkm÷j`gk. Win Mu`s Vktksâ? Higumtia ad `njdn`drâi, Tn`vdrs`aia Iut÷nkbi ad Win Mu`s Vktksâ. Gibpks Irinai, A. H. (5696). @ntrkaugg`÷n i mi C`arkmkjâi Treini. Win Mu`s Vktksâ.

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