ƒƒƒ‘ƒƒ—ƒ‌ƒ‘ƒ ƒ“ƒ...

download ƒƒƒ‘ƒƒ—ƒ‌ƒ‘ƒ ƒ“ƒ ƒ›ƒƒ—ƒ”ƒ›ƒƒ¢ƒƒ™ƒ£ƒ ƒ ƒƒ¢ƒƒ¢ƒƒƒ¢ƒƒ™ƒ

If you can't read please download the document

  • date post

    06-Aug-2015
  • Category

    Documents

  • view

    1.408
  • download

    126

Embed Size (px)

description

ომარ ფურთუხია, ზურაბ ციგროშვილი, ქეთევან მანჯგალაძე.

Transcript of ƒƒƒ‘ƒƒ—ƒ‌ƒ‘ƒ ƒ“ƒ...

omar furTuxia,zurab cigroSvili,qeTevan manjgalaZealbaToba da maTematikuristatistika(leqciebis kursi qimiis, biologiis da sicocxlisSemswavleli mecnierebebis mimarTulebebisstudentebisaTvis)T s u2leqciebiskursSigadmocemuliaTanamedrovealbaTobisTeoriisada maTematikuri statistikis ZiriTadi cnebebi da faqtebi, romlebicaucilebelia rTuli qimiuri da biologiuri procesebis Sesaswavladda maTTvis met-naklebad adekvaturi modelebis asagebad. masSi warmod-genilia maTematikuri statistikis iseTi nawilebi, rogoricaa Sefaseb-isa da hipoTezaTa Semowmebis Teoria erTi da or amokrefiani amocane-bisaTvis, dispersiuli da regresiul-korelaciuri analizi, kategori-uli tipis monacemebis analizi da statistikis araparametruli meTo-debi.leqciebis kursi gankuTvnilia iv. javaxiSvilis saxelobis Tbilis-is saxelmwifo universitetis, qimiis, biologiisa da sicocxlis Sems-wavlelmecnierebaTamimarTulebebisstudentebisaTvis; igisasargeb-loiqnebasxvaumaRlesisaswavleblebis(magaliTad,samedicinodateqnikuri universitetis Sesabamisi mimarTulebebis) studentebisa dastatistikis gamoyenebiTi aspeqtebiT dainteresebuli sxvadasxva pro-filis specialistTa farTo wrisaTvis.3winasityvaobawinamdebare leqciebis kursi albaTobasa da maTematikur stati-stikaSi(qimiis,biologiisadasicocxlisSemswavlelmecnierebaTamimarTulebebis meoTxe kursis studentebisaTvis) warmoadgens am mima-rTulebaTa studentebisaTvis gankuTvnili umaRlesi maTematikis sagnisSemadgenelisamikursidan(kalkulusi,diferencialurimodelebi,albaTobadamaTematikuristatistika)mesamenawils.isefuZneba2007-2009 wlebSi aRniSnuli mimarTulebebis (da agreTve socialurda politikur mecnierebaTa da ekonomikisa da biznesis mimarTulebeb-is) studentebisTvis albaTobis Teoriasa da maTematikur statistika-Si wakiTxul leqciebs. misi Sedgenisas, garda iv. javaxiSvilis saxel-obis Tbilisis saxelmwifo universitetSi am kuTxiT arsebuli gamoc-dilebisa, gamoyenebulia Sesabamisi kursis harvardis samedicino saja-ro skolaSi (aSS) wakiTxvis gamocdileba. leqciebis kurss Tan erTvisqarTul da inglisur enebze silabusi saTanado ZiriTadi da damxmareliteraturiT da leqciebis mixedviT paragrafebis miTiTebiT. leqcieb-is kursi sasargeblo iqneba rogorc iv. javaxiSvilis saxelobis Tbi-lisis saxelmwifo universitetis, aseve qimiis, biologiis da sicocx-lis Semswavlel mecnierebaTa mimarTulebebis sxva umaRlesi saswavle-blebis studentebisa da magistrantebisaTvis.o. furTuxiaTbilisi, marti,20094SesavalialbaTobis Teoria warmoadgens maTematikis dargs, romelic Sei-swavlisiseTieqsperimentebis(movlenebis)maTematikurmodelebs,romelTa Sedegebi calsaxad ar ganisazRvreba cdis pirobebiT. aseT eq-sperimentebs ewodebaT SemTxveviTi eqsperimentebi. SemTxveviTi eqsperi-mentebia: monetis agdebis Sedegi, mizanSi srolisas miznis dazianeba anardazianeba, xelsawyos muSaobis xangrZlivoba, satelefono sadgurSigamoZaxebaTaricxvi,avto-sagzaoSemTxvevaTaraodenoba,arabejiTistudentis mier gamocdis Cabarebis Sedegi, valutis kursi rom ar Ca-mova garkveul niSnulamde da sxva.saWiroa aRiniSnos, rom albaTobis Teoria ikvlevs ara nebismi-er SemTxveviT eqsperiments, aramed mxolod iseT eqsperimentebs, rom-lebic xasiaTdebian statistikuri mdgradobis anu sixSireTa mdgrado-bis TvisebiT: sixSireebii nn Ai/ ) ( (sadacin i -ur seriaSi eqsperimen-tebis ricxvia, xolo ) ( Ain_ ki Axdomilebis moxdenaTa raodeno-ba am seriaSi) axlos arian erTmaneTTan (mcired gansxvavdebian erTman-eTisagan an raime saSualo sidididan) yovelTvis rogorc kiinricx-vebi iqnebian sakmaod didebi. magaliTad, v. feleris wignSi moyvaniliamonetisagdebis10seriaSi( 10 ,... 1 = i ),sadacTiTeulseriaSi1000 =ineqsperimentia, gerbis mosvlaTa ) " ("ginricxvis Semdegi mo-nacemebi: 501, 485, 509, 536, 485, 488, 500, 497, 494, 484. cxadia,rom aq fardobiTi sixSireebi axlosaa erTmaneTTan, da maSasadame, eqs-periments, romelic mdgomareobs simetriuli monetis agdebaSi, gaaCniasixSiris mdgradobis Tviseba.g. krameris mier moyvanili monacemebi 1935 wels SveciaSi daba-debuli axalSobilebis Sesaxeb (sadac n _ axalSobilTa raodenobaa,xolo / mn_ vaJebis dabadebis fardobiTi sixSire) ase gamoiyureba:Tveebi I II III IV V VIn 7280 6957 7883 7884 7892 7609m/n 0.515 0.510 0.510 0.529 0.522 0.518Tveebi VII VIII IX X XI XII suln 7585 7393 7203 6903 6552 7132 88273m/n 0.523 0.514 0.515 0.509 0.518 0.527 0.517miuxedavad imisa, rom axalSobilTa saerTo raodenoba icvlebawlisganmavlobaSi,vaJebisdabadebisfardobiTisixSiresakmaodmdgradad meryeobs 0.517 saSualo mniSvnelobis irgvliv.analogiuri statistikuri kanonzomierebebi aRmoCenil iqna me-18saukuneSi demografiul monacemebSi axalSobilTa statistikis Sesw-5avlisas, sikvdilianobis statistikis Seswavlisas, ubdur SemTxvevaTastatistikis Seswavlisas da a. S. (rac, Tavis mxriv, sakmaod efeqtur-ad gamoiyebneboda sadazRvevo kompaniebis saqmianobaSi). mogvianebiT, me-19 saukunis bolos da me-20 saukunis dasawyisSi axali statistikurikanonzomierebebi aRmoCenil iqna fizikaSi, qimiaSi, biologiaSi, sicoc-xlis Semswavlel mecnierebebSi, ekonomikaSi da sxva mecnierebebSi. amkanonzomierebebsmivyavarTalbaTobisstatistikurigansazRvrisaken:ricxvs, romlis irgvlivac irxeva Axdomilebis fardobiTi sixSire,ewodeba Axdomilobis albaToba da aRiniSneba ) ( A PsimboloTi. maT-ematikuri dasabuTeba imisa, rom fardobiTi sixSire axlosaa albaTob-asTan moyvanilia iakob bernulis cnobil TeoremaSi, romelic albaTo-bis TeoriaSi cnobilia agreTve did ricxvTa kanonis saxelwodebiT.aRsaniSnavia,romyvelaSesaZloeqsperimentiSeiZlebagaiyossam kategoriad: I. eqsperimentebi sruli mdgradobiT, sadac saerTodaraa ganuzRvreloba; II. eqsperimentebi sadac ara gvaqvs sruli mdgra-doba,magramarisstatistikurimdgradoba; III.eqsperimentebisadacstatistikuri mdgradobac ki ara gvaqvs.pirvel jgufs miekuTvneba umravlesoba eqsperimentebis, romleb-ic aRiwerebian sabunebismetyvelo mecnierebebis (fizika, qimia, biolo-gia) klasikuri kanonebiT da maTi Seswavla xdeba albaTobis Teoriisgamoyenebis gareSe. mesame kategoriisaTvis albaTobis Teoria gamousad-egaria. meore jgufi warmoadgens swored albaTobis Teoriis gamoyene-bis ares. TviTon albaTobis Teoriis mier gadasawyveti amocanebi iyo-fa or did jgufad. pirveli jgufis amocanebs SeiZleba vuwodoT amo-canebi rTuli xdomilebebis albaTobebis gamoTvlaze, roca cnobiliamartivi xdomilebebis albaTobebi.amocanebis meore jgufi garkveuli azriT pirveli jgufis amo-canebis Sebrunebulia. aq eqsperimentebis seriis Sedegebis safuZvelzeraime gziT unda SevafasoT martivi xdomilebebis albaTobebi. vinaidan,martivixdomilebebisalbaTobebiucnobiaimamocanebSi,romlebicpraqtikaSi warmoiSoba, amitom amocanebis es jgufi gansakuTrebiT sai-nteresoagamoyenebebisTvalsazrisiT.albaTobisTeoriisimnawils,romelicaxdensmeoregjufisamocanebiszustdasmasdaikvlevsmaTi amoxsnis meTodebs, maTematikuri statistika ewodeba.maTematikuri statistika es aris maTematikis dargi, romelicSeiswavlisstatistikurimonacemebissistematizaciis,analizisadagamoyenebis meTodebs Teoriuli da praqtikuli daskvnebis miRebis miz-niT. igi Sedgeba ori nawilisagan: aRweriTi (deskrifciuli) statist-ika da statistikuri daskvnebis Teoria. misi meTodebi albaTobis Teo-riazeadafuZnebuli.albaTobisTeoriawarmoadgensxidsaRweriTstatistikasa da statistikuri daskvnebis Teorias Soris, igi saSua-lebas iZleva gaviazroT, Tu rogor iqmneba da gamoiyeneba statistiku-6ri procedurebi, rogor SeiZleba aviciloT Tavidan am meTodebis ara-swori gamoyeneba.albaTobis Teoriis rogorc mecnierebis ganviTareba miekuTvnebame-17 saukunis meore naxevars da dakavSirebulia paskalis (1623-1662),fermas (1601-1665) da hiugensis (1629-1695) saxelebTan, Tumca calke-uli amocanebi, romlebic dakavSirebuli iyo azartul TamaSebSi Sanse-bis daTvlasTan, XV-XVI saukuneebSic ganixileboda italieli maTema-tikosebismier(kardano,paColi,tartaliadasxva).ammecnierebisWeSmaritiistoriakiiwyebai.bernulis(1654-1705),p.laplasisa(1749-1827) da s. puasonis (1781-1840) Sromebidan. maTematikuri stat-istika rogorc mecniereba iwyeba k. gausis (1777-1855) Sromebidan. ma-Tematikuri statistikis ganviTarebaSi didi wvlili miuZRviT k. pirs-ons (1857-1936), r. fiSers (1860-1962), e. neimans (1894-1977), a. kol-mogorovs, n. smirnovs (1900-1966), a. valds (1902-1950) da sxvebs.saqarTveloSi albaTobis Teoriisa da maTematikuri statistikisswavlebistradiciassafuZvelidaudoandriarazmaZem(1889-1929),romelickiTxulobdaleqciebiskurssaxladdaarsebulTbilisisuniversitetSi,xolomaTematikisamdargisganviTarebassafuZveliCauyara gvanji maniam (1918-1985), masve ekuTvnis pirveli qarTuli sa-xelmZRvaneloebidamonografiebiammimarTulebiT.aRsaniSnavia,romsaqarTveloSi albaTobis Teoriisa da maTematikuri statistikis ganvi-Tarebas ara marto wminda maTematikuri gamokvlevebiT, aramed gamoyen-ebiTixasiaTiskvlevebiTacRrmakvalidaaCniarevazCitaSvilma(1942-1995).maTematikuri statistika farTod gamoiyeneba teqnikur gamokvl-evebSi, sicocxlis Semswavlel mecnierebebSi, ekonomikaSi, sabanko sfe-roSi,marTvis(menejmentis)TeoriasadapraqtikaSi,sociologiaSi,medicinaSi, geologiaSi, istoriaSi da a. S. dakvirvebebis, gazomvebis,eqsperimentebis Sedegebis damuSavebasa da analizTan saqme gvaqvs rog-orc adamianis praqtikuli moRvaweobis yvela sferoSi, ise samecnierokvlevebisyvelamimarTulebaSi.statistikisaRwerilobiTimxaridannaTeli xdeba, Tu adamianis moRvaweobis romel mxares exeba esa Tu isamocana:ekonomikas,demografias,biologias,medicinas,sociologiasda a.S. Sesabamisad, SeiZleba visaubroT ekonometrikaze, demografiulstatistikaze, biometriaze, bio-samedicino statistikaze, statistika-ze socialur mecnierebebSi da a.S., rogorc statistikis erTi Sexedv-iTsxvadasxvasferoebze.sinamdvileSi,yovelimaTganiwarmoadgensmonacemTa sxvadasxva bazas, romelTa damuSaveba da analizi xdeba maTe-matikuri statistikis meTodebis gamoyenebiT.7silabusisaswavlokursisdasaxelebaalbaTobadamaTematikuristatistikaqimiis,biologiisadasicocxlisSemswavlelimecnierebe-bisTvissaswavlokursis kodisaswavlokursisstatusikursi gaTvaliswinebulia qimiis, biologiisa da sic-ocxlisSemswavlelimecnierebebismeoTxekursisstudentebisTvis, rogorc savaldebulosaswavlokursisxangrZlivobaerTi semestriECTS-saswavlokursikreditebi6krediti:60sakontaqtosaaTi(leqcia30saaTi,praqtikuli30saaTi,laboratoriulisamuSao(cxrilis gareT)) 90 saaTi damoukidebeli muSaobis-aTvisleqtorebi pro