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1/131

Arzurui ]a`nf` nfvarsftasf

stltfstfa Kfrf

Wrho. Mr. roln @LVILU

stltfstf` va jlsj`

Arzurui ]a`nf` nfvarsftasfIdanmfsjf` Ol`jtasf

Il`fna Idanmfsjff Bji

aaimarsnhtjlrf.chi

8/10/2019 Olaslk Ve statistik - Erzurum Teknik niversitesi Ders Notlar

2/131

Arzurui ]a`nf` nfvarsftasf

stltfstfa KfrfMars Ioramlt

stltfstfa Kfrf

L`jlyc stltfstf`

Iar`azf Afjfi va Mljil jjarf

Hjlsj` (dtfilj)

Lnl`tja Mljijlr

rna`jaia Wjlnjlr va Mljijlr

]ldifnjar

Dfphtaz ]astjarf

_lrylns Lnljfzf

Rakrasyhn va @hrajlsyhn Lnljfzf

aaimarsnhtjlrf.chi

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3/131

Arzurui ]a`nf` nfvarsftasf

stltfstfa KfrfBfjfi va Hjlsj`

Bfjfi, shnsuz slyml va h` `lril` nasna va hjlyjlrmln hjuln avranfn `lvrlnilsnsljlil` zara0nasna va hjlyjlr shyutjlil`snojlnmril`,bu snojlrn ffnma`f va lrlsnml`f fjf`fjarf kanaj dltjlryjl bujil`yhjunl kftia`tamfr.

Bu ftfblrjl, bfjfifn `hnusu ta` nasna va ta` hjlymafj, nasna va hjly thpjuju`jlrmr.

Avranma`f hjlyjlrn daian dfbfrf mfarfna aft mafjmfr. Lrljlrnml mlfil lz yl ml h`olr`jlr bujunil`tlmr.

Nasna va hjlyjlr zliln farfsfnma sra`jf bfr maffi va bl`ljli kstarfrjar.

rnafn5Lyn olbrf`lml pa paa ylpjln f`f hthihbfjfnf`f aja`trf` lipujnn mlylnil srajarf aft hjilylcl`tr.

aaimarsnhtjlrf.chi

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4/131

Arzurui ]a`nf` nfvarsftasf

stltfstfa KfrfBfjfi va Hjlsj`

Avranma krjan olr`jj` va aftjfjffn namanjarf bfjfisaj lmln 3 kruptl thpjlnil`tlmr5

8/10/2019 Olaslk Ve statistik - Erzurum Teknik niversitesi Ders Notlar

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Arzurui ]a`nf` nfvarsftasf

stltfstfa KfrfBfjfi va Hjlsj`

h` `lril` hjln avranma`f nasna va hjlyjlr l`jlil` va zajjf`ja kajaca`ta`fmuruijlrn ncaman slptlil` ffn bfjfifn ratabfjmff bfrfncf tr at`anjar yatarjf

hjilil`tlmr.

Bunun ylnnml f`fncf va nc tr at`anjarf ma mf``lta ljil` zhrunjujuu vlrmr.

Bfjfniayan vayl manatjanaiayan at`anjar rlstkaja at`anjarja bfrjf`ta,

thpjucl hjlsj` hjlrl` krjia`ta,hjlsj` `urli va yntaijarf fja fncajania`ta,fstltfstf`saj yntaijarja maarjanmfrfjia`tamfr.

aaimarsnhtjlrf.chi

8/10/2019 Olaslk Ve statistik - Erzurum Teknik niversitesi Ders Notlar

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Arzurui ]a`nf` nfvarsftasf

stltfstfa KfrfHjlsj`-stltfstf` @urljjlr

Avranma iaymlnl kajan dar ayfnbfr namanf vlrmr,namansfz bfr ayhjilz. rnafn,

dlvlyl ltjlnbfr ilmanf plrl yara mar,s`trjlnklz aparjarfnablsnylplr, vs.Bu hjlyjlrnnamanjarf0 yar a`fif,klz ihja`jjarfnfndlra`atf, hjlrl` bfjfnia`tamfr.

Ol`lt bu hjlyjlr zarfnamldl lyrntjva zajbfjkf amfnia`, maarjarfnfva shnujlrnncaman `asfn bfr a`fjma rania` fstarsa`, bukn` bfjkfjarfifzja bllrlilyz.rnafn yliurun na zliln yllcln, blrlen na jma mhjlcln, bfr il`fnlnn

vayl aja`trf` lipujnnmlylnil srasfnf,iayva bldasfnfnvarfifnf, bfr dlstlnn`lknma fyfjaacafnf rancfnfn bfr snlvml ljlcl nhtu, bfr iln shnucunu ncaman`asfnjf`ja bfjaiayfz.

Szamfjan maarjarfnlsjbfjabfjfrfz8 ]li va `asfn hjlrl` bfjiaifz ii`nimr8Bu bfjkfjarf, hjlymln nca slptlil` va `asfn maarjar dljfnma varia` bukn` bfjfi

mzayfnmaii`nmafjmfr!

Bukn` bfjkfjarja slmaca bfr tldifnma bujunil` ii`nmr.

aaimarsnhtjlrf.chi

8/10/2019 Olaslk Ve statistik - Erzurum Teknik niversitesi Ders Notlar

7/131Arzurui ]a`nf` nfvarsftasf

stltfstfa Kfrf

]ldifn, kaifta`f bfjkf va manayjara mlylnlrl` kajaca` zarfna bfr ylrkylvlril`tr.

Vlpjln tldifnfn zajjf`jarf5

Bu ylrk `asfn va tli mhru hjilyp, lncl` hjls bfr maar tlil`tlmr.

Bl`l bfr folmayja, bajfrjf bfr kvan mzayfnma (rnafn %61 vayl %66 hjlsj`jl) mhrumur.

Bu kvan mzayfnfn mnml`f dltl ply fja (rnafn %1 vayl %< hjlsj`jl) ylnjtr.

Bu ylrk tli va `asfn bfr ta` maar dljfnma varfjaiaz. Lncl`, ba`janan bfr muruiun

hjlsj (rnafn %17 hjlsj`jl ylz) yl ml hjls jjarfn hrtljlil va snr maarjarf

(rnafn, 17 `ffjf` bfr snotl rancf bhyjlrnn hrtljlils %61 kvan mzayfnma

8/10/2019 Olaslk Ve statistik - Erzurum Teknik niversitesi Ders Notlar

8/131Arzurui ]a`nf` nfvarsftasf

stltfstfa Kfrf

Bu yhjmln ajma amfjan bfjkfjara mlylnlrl` kanajjaia ylpil` va hjlyjlr lrlsnml`f

fjf`fjarfn hjlsj`jlrn bajfrjaia` va kanaj `urljjlr dljfnma hrtlyl `hyil`, byjacabfjfia `lt`ml bujunil` ii`nmr. Ol`lt, bu `urljjlr mhlj `urljjlr kfbf `asfn vamafiazfjf`fjarfkstaraiazjar.

Rlstjlntyl blj hjlyjlrn fncajaniasfnma5uykujlnln yntaijara fstltfstf`saj yntaijar,

`ujjlnjln slyjlrl fstltfstf`bu slyjlr lrlsnml`f blntjlrl fstltfstf`saj blntjlrujljln bfjfi `urljjlrnl ml fstltfstf`saj `urljjlr

lm varfjia`tamfr.

Hjlsj`-stltfstf` @urljjlr

aaimarsnhtjlrf.chi

8/10/2019 Olaslk Ve statistik - Erzurum Teknik niversitesi Ders Notlar

9/131Arzurui ]a`nf` nfvarsftasf

stltfstfa Kfrf

stltfstf saj bfjkfjar lncl` h` slyml`f hjly vayl nasnanfn kzjaniasf va fncajaniasf

fja ajma amfjabfjfr.Bu yhjmln ajma amfjan bfjkfjar va ujljln `urljjlr ml lncl` h` slyml`f hjly va nasnaffn kaarjfmfr.]a` bfr hjlyl uykujlnlilzjlr.

Hjlsj`-stltfstf` @urljjlr

rna`5Vlz kajia hjlsj %17 maia`ja, f`f `az plrlltnmlnbfrfnfn `asfnjf`ja ylzkajacafsyjanaiaz.

Lncl`, plrl ltn h` `az yfnajamffifz zliln,

bunjlrmln yl`jl` ylrsnn ylz kajacaf ncaman`astfrfjabfjfr.

aaimarsnhtjlrf.chi

8/10/2019 Olaslk Ve statistik - Erzurum Teknik niversitesi Ders Notlar

10/131Arzurui ]a`nf` nfvarsftasf

stltfstfa Kfrf

stltfstf`saj `urljjlrml rlstjlntyl blj bfr hjlyn h` (shnsuz) `az yfnajaniasfyja

olr`jjlilyl yhj lln rlstkaja namanjarfn bfrbfrfnf mankajayacaf mnjia`tamfr.Byjaca, h` `az ta`rlr dljfnma, bajfrjf va naijf hjln namanjarfn at`fsfnfn hrtljlilmaarhjlrl` krjabfjacaf`lbuj amfjia`tamfr (by`slyjlrylsls).

Hjlsj`-stltfstf` @urljjlr

rna`5"Wrhblbfjfty lnm Stltfstfcs wftd Lppjfcltfhn"

`ftlbnn ylzlr Wakky ]lnk Strlftfn hjunun?77 zlr ltnl `lrj`

8/10/2019 Olaslk Ve statistik - Erzurum Teknik niversitesi Ders Notlar

11/131Arzurui ]a`nf` nfvarsftasf

stltfstfa Kfrf

Bfjfisaj lnjli fja fstltfstf`5

phzftfo bfjfijarfn taiajf hjlnkzjaijarfn

ylpjils

, varfjarfnthpjlnils

, lnljfzf vayhruiu ffn kara`jf yntaijarfn kajftfrfjfp uykujlnils fja urlln, shnutl

varfjarman kfmfjara` bujunln hjlsj` manayfijarf fja hbea`tfo `lrlr variama naijf

rhjhjln bfjfi mljmr.

stltfstf`saj yntaijarfn kravf0

Bfr lrltrilnn an lz kfmarja va an at fn yhruijlily sljlylbfjaca` bffima pjlnjlnils,Marjanan slyslj bfjkfjarfn mzanjaniasf va maarjanmfrfjiasf,Ajma amfjan bfjkfjarfn yhruijlnils va shnu `lrjils

yhjjlrn bajfrjaia` va ratia`tfr

stltfstffn ]lni

aaimarsnhtjlrf.chi

8/10/2019 Olaslk Ve statistik - Erzurum Teknik niversitesi Ders Notlar

12/131Arzurui ]a`nf` nfvarsftasf

stltfstfa Kfrfstltfstffn ]lrfdasf

Hjlsj` (Wrhblbfjfty) fja fjkfjf fj` `lytj bfjkf lns hyunjlrnml rlstjlnil`tlmr.

Hjlsj` fja fjkfjf ljiljlr0

8/10/2019 Olaslk Ve statistik - Erzurum Teknik niversitesi Ders Notlar

13/131Arzurui ]a`nf` nfvarsftasf

stltfstfa Kfrfstltfstffn Snojlnmrjils

_arfjarfn maarjanmfrfjiasfnma `ujjlnjil muruiunl kra0

8/10/2019 Olaslk Ve statistik - Erzurum Teknik niversitesi Ders Notlar

14/131Arzurui ]a`nf` nfvarsftasf

stltfstfa KfrfMaf`an ]fpjarf

Lrltriljlrml fjkfjanfjan `lrl`tarfstf`jarfn taspftf ji va/vayl slyi yhjuyjl ylpjr.jiva/vayl slyiyhjuyjl ajma amfjan bfjkfjara varfmanfr.

_arfjarfn nftajar ffn `asfn maarjarf bfjfniaz hjup, kanajjf`ja olr`jmr. Bu zajjf`fstltfstf`ta rlsslj (lns rlstkaja) maf`an `lvrlin hrtlyl `lril`tlmr. @anmfsfnaolr`j maarjar ltlnln T, V, U kfbf dlrojarja folma amfjan h`ju`jlr rlsslj maf`an hjlrl`bfjfnfr. Szkajfif, bfr snotl`f rancfjarfn bhyjlr va lrj`jlr lyr bfrar rlstkajamaf`anmfr. n`,rancfjarfnbu vlsojlr`ffjarlrlsnmlslbft hjilyp,mafia`tamfr.

aaimarsnhtjlrf.chi

8/10/2019 Olaslk Ve statistik - Erzurum Teknik niversitesi Ders Notlar

15/131Arzurui ]a`nf` nfvarsftasf

stltfstfa Kfrf_arfjarfn Dlsslsfyatf

stltfstf`saj maarjanmfriaya ljnlcl` varfjarfn dlsslsfyatf va mhruju` maracasf y`sa`

hjiljmr. Bu namanja, lrltriljlrn yrtjiasfnma `ujjlnjln ljat va a`fpilnjlrndlsslsfyatf fja ljlnjlrnbfjkf va mf``ltf naijfmfr.

Lyn`lrl`tarfstf` `lbl bfr j ljatf (ajf` iatra) fja jjabfjacafkfbf, mldl dlssls bfrj ljatf (if`rhiatra) fja ma jjabfjfr. jijarma `ujjlnjlcl` ljatjarfn dlsslsfyatmaracasf jjannasnajarfn by`jnava `hnunun naifnakramaffr.

Rl`lijlrn dlsslsfyatf hnmlj` slys fja bajfrjanfr. Dlsslsfyatfn h` `` tutujilskvanfjfrjf` va maf`anjffn `lybhjilsnl, karafnman by` tutujils ml rl`lih`juunamanfyja fjaidltljlrnlyhj llclnmlntlvsfya amfjiaz.

Bunmln mhjly, blz maarjanmfriajarma varfjarfn yuvlrjltjils olymlj hjlbfjfr.Vuvlrjltil fjaifnmaasls hjlrl`0 ltjlcl`dlnama bujunln rl`li 1 vayl mldl by`fsa bfr nca`fdlna maarf< lrtrjr,ltjlcl`dlnama bujunln rl`li 1man``fsa bfrnca`fdlna maarflyn`ljr. rnafn,2.?=4; slyshnmlj`dlna tlilsdljfnma2.?=6, f`f hnmlj`dlna tlilsdljfnma 2.?1, bfr hnmlj`dlna tlilsdljfnma fsa 2.?hjlrl` ljnlbfjfr.

aaimarsnhtjlrf.chi

8/10/2019 Olaslk Ve statistik - Erzurum Teknik niversitesi Ders Notlar

16/131Arzurui ]a`nf` nfvarsftasf

stltfstfa KfrfHrlnjlr va Vzmajar

Bfr prhbjaifn folmasfnma iutjl` varf maarjarfnf varia`tansa hrln va yzma maarjarfnf

varia` mldl lymnjltc hjil`tlmr.

rna`5Vly filj aman bfr olbrf`lml knj`hrtljlil

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17/131Arzurui ]a`nf` nfvarsftasf

stltfstfa KfrfLnl`tja va rna`

Lrltrjln bfr `hnuyl lft varfjarman `asfn shnujlrl ujljil` fstanfyhrsl, `hnuyl lftbtn ajailnjlrn fncajaniasf kara`fr.

Lrltrilyl lyrjln plrl va zlilnn snrj hjils namanfyja bu murui fi`lnszmr.stltfstf saj iathtjlr ylrmiyjl `hnu fja fjkfjf ajailnjlrmln rlstkaja safjif snrjslyml rnafn maarjanmfrfjiasf fja ajma amfjan shnujlr bajfrjf bfr kvan mzayfnma ti`tjaya kanajjatfrfjabfjfr.

zarfnma murujln `lrl`tarfstf`jarja fjkfjf btn ajailnjlr ffna ljln thpjujul lnl`tja(phpujlsyhn) manfr.

Lnl`tjaman rlstkaja a`fjan va zarfnma fncajaia ylpjln snrj ajailnjlr thpjujuunlfsa rna`manfr.

Szkajfif, ]r` fnslnnn vcut jjarf bajfrjania` fstanfyhrsl, j`anfn btn fnslnjlrzarfnma ji ljil` yarfna j`ayf taisfj amacaf mnjan blz bjkajarman rlstkajarna`jar safjara` bunjlr zarfnma ji ylpjr va ajma amfjan shnujlr kanajjatfrfjfr.

aaimarsnhtjlrf.chi

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18/131Arzurui ]a`nf` nfvarsftasf

stltfstfa KfrfLnl`tja va rna`

_lrjln shnujlrn tutlrjj safjan rnafn lnl`tjayf taisfj atiasfna bljmr.

]aisfjf at`fjayan an naijf f`f dusus5rnafn by`jrlstkaja safjif hjilsmr.

Lrltriljlrml zliln, plrl, a`fpiln va dlsslsfyat bl`inmln lnl`tja yarfna rna`zarfnmaljjr. rnafnby`jfsa szamfjan bu ol`trjarasls ljnlrl`bajfrjanfr.

Daslpjliljlrml `ujjlnjlnsaibhjjar fsa lnl`tjava rnaakraolr`jj`kstarfrjar.Lnl`tjama

L`jlil

rna`ta

N Ajailn slys n

Hrtljlil

W Hrln p

2 _lrylns S2

Stlnmlrt slpil S

x

Hrtljlilnn stlnmlrt dltls

Sx

Rakrasyhn `ltslys b

@hrajlsyhn `ltslys r

T

Lnl`tjaya lft N, , 2, ... kfbf maarjara plrliatramanfjia`tamfr.Lnl`tja plrliatrajarfnfn bfrar tldifnf hjln n, T, S2, ... b kfbf rna` maarjarfna mafstltfstf`manfjia`tamfr.

aaimarsnhtjlrf.chi

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Arzurui ]a`nf` nfvarsftasf

stltfstfa KfrfKajaca` marsfn `hnusu

L`jlyc stltfstf`.

aaimarsnhtjlrf.chi

8/10/2019 Olaslk Ve statistik - Erzurum Teknik niversitesi Ders Notlar

20/131roln @lyilz Arzurui ]a`nf` nfvarsftasf

L`jlyc stltfstf`

Wrho. Mr. roln @LVILU

stltfstf` va jlsj`

Mars 25 L`jlyc stltfstf`

aaimarsnhtjlrf.chi

8/10/2019 Olaslk Ve statistik - Erzurum Teknik niversitesi Ders Notlar

21/131roln @lyilz Arzurui ]a`nf` nfvarsftasf

L`jlyc stltfstf`]lni

ncajaia shnucu ajma amfjan dli varfjarfn fstltfstf`saj yntaijar `ujjlnjlrl`

zatjaniasf l`jlyc fstltfstff `hnusumur.

L`jlyc fstltfstf`ta `ujjlnjln yntaijar5

Ora`lns ]lbjhjlr

a`fjjar va Krlof`jarDfsthkrli va Ora`lns WhjfklnjlrStun va Wlstl Krlof`jarf

aaimarsnhtjlrf.chi

8/10/2019 Olaslk Ve statistik - Erzurum Teknik niversitesi Ders Notlar

22/131roln @lyilz Arzurui ]a`nf` nfvarsftasf

L`jlyc stltfstf`Ora`lns ]lbjhjlr

@ujjlnjlnan ylyknyntaijarmanbfrfmfr.

rna` Ora`lns ]lbjhsu

aaimarsnhtjlrf.chi

8/10/2019 Olaslk Ve statistik - Erzurum Teknik niversitesi Ders Notlar

23/131roln @lyilz Arzurui ]a`nf` nfvarsftasf

L`jlyc stltfstf`Ora`lns ]lbjhjlr

_arfjarf ora`lns tlbjhjlr ylrmiyjl snojlnmrilnn ylrlrjlr yja

zatjanabfjfr5

jkfjfmaf`anfnmljidl``nmlbfjkf ljnlbfjfr._arfjarfn dlnkf maarjaratrlonmlkrupjlnmkrjabfjfr.Hrtljlil, stlnmlrt slpil va vlrylns kfbf maarjar mldl `hjlydaslpjlnlbfjfr.

Bu ylrlrjlrnl `lrn varfjarfn snojlnmrjils srlsnml (zajjf`ja snolrlj`jlrnn kanf tutujils dljfnma) bfjkf va dlsslsfyat `lyb hjil`tlmr.n`,dardlnkf bfr snonlrljffnamanolr`jmaarjarslmaca h lrljnhrtl maarffja taisfj amfjfrjar.

aaimarsnhtjlrf.chi

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roln @lyilz Arzurui ]a`nf` nfvarsftasf

L`jlyc stltfstf`Ora`lns ]lbjhjlr

Ora`lns tlbjhjlrnnmzanjaniasfnmallml`fsrlfzjanfr5

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25/131

roln @lyilz Arzurui ]a`nf` nfvarsftasf

L`jlyc stltfstf`Ora`lns ]lbjhjlr

Ora`lns tlbjhjlrnnmzanjaniasfnmallml`fsrlfzjanfr5

?. Sno jfiftjarfnfn hrtljliljlr ljnlrl` sno maarjarf (sno hrtljliljlr)bajfrjanfr.

;. _arfjar tlrlnlrl` dar snolmaca`varf slys(ora`lns) bajfrjanfr.

Ora`lns tlbjhsunml`f dar bfr sno ffn nfspf (hrlnslj) ora`lns, a`jaiajf ora`lns vaa`jaiajf nfspf(hrlnslj) ora`lns maarjarf daslpjlnr.

Nfspf Ora`lns5 bfr snon ora`lnsnn (n) thpjli varf slysnl (N) bjnp,

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roln @lyilz Arzurui ]a`nf` nfvarsftasf

L`jlyc stltfstf`Ora`lns ]lbjhjlr

rna`

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27/131

roln @lyilz Arzurui ]a`nf` nfvarsftasf

L`jlyc stltfstf`Ora`lns ]lbjhjlr

rna` < UI5

MK9=.;-

8/10/2019 Olaslk Ve statistik - Erzurum Teknik niversitesi Ders Notlar

28/131

roln @lyilz Arzurui ]a`nf` nfvarsftasf

L`jlyc stltfstf`Ora`lns ]lbjhjlr

rna` < UI5

Ora`lns tlbjhsunun tlrlilstununl bl`jmnml varfjarfn dlnkf maarjaratrlonml yhunjlt va varf krubunl lft mljin a`jf `lblcl krjia`tamfr

aaimarsnhtjlrf.chi

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29/131

roln @lyilz Arzurui ]a`nf` nfvarsftasf

L`jlyc stltfstf`a`fjjar va Krlof`jar

Lnjlij bfjkfjarf `lrlbfjia` ffn a`fjjarfn

va krlof`jarfn fzfifnma a`sanjarfn hrlntjhjilsnl va kara`jf l`jlyc bfjkfjarfbujunmurilsnl mf``lt amfjiajfmfr. _arfjarfa`fj va krlof`jarja kstarianfn ylrlrjlrllml`fkfbf zatjanabfjfr5

Lnjljlbfjfrjf` lrtrjr.Mf``lt a`fjaca` dususjlr bajfrtfjfr.Mljin bffif dl``nml bfjkf sljlnr.]ldifn `hjlyjlr

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