Tsu-2011 - ieeetsu

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normaluri ganawilebis cxrilis pirvel svetSi movZebnoT ricxvi 1.1, xolo pirvel striqonSi ki – ricxvi .08. 1.1-is Sesabamisi striqonisa da .08-is Sesabamisi svetis gadakveTaze vpoulobT ricxvs – 0.8810. amitom saZiebeli albaToba iqneba PN ( (0,1) 1.18) 0.8810 anu 88.10%. magaliTi 2. vipovoT albaToba imisa, rom standartuli normaluri SemTxveviTi sidide naklebia -0.63-ze, PN ( (0,1) 0.63) ? amoxsna. am SemTxvevaSi z 0.63 da saZiebeli albaToba iqneba P( N(0,1) 0.63) P( N(0,1) 0.63) 1 (0.63) 10.7357 0.2643 anu 26.43%. magaliTi 3. vipovoT albaToba imisa, rom standartuli normaluri SemTxveviTi sidide metia -1.48-ze, PN ( (0,1) 1.48) ? amoxsna. am SemTxvevaSi z 1.48 da gamosaTvlelia normaluri ganawilebis wiris qveS -1.48-is marjvniv moTavsebuli aris farTobi. Tu visargeblebT normaluri ganawilebis simetriulobiTa da () z funqciis cxrilebiT, miviRebT: P( N(0,1) 1.48) P( N(0,1) 1.48) (1.48) 0.9306 . SeniSvna. SegviZlia visargebloT sawinaaRmdego xdomilebis albaTobis gamosaTvleli formuliT da maSin magaliTi daiyvneba wina magali- Tze: P( N(0,1) 1.48) 1 P( N(0,1) 1.48) 1 P( N(0,1) 1.48) 10.0694 0.9306 . 71
magaliTi 4. vipovoT albaToba imisa, rom standartuli normaluri SemTxveviTi sidide moTavsebulia SualedSi -1.65-sa da 1.65-s Soris, P( 1.65 N(0,1) 1.65) ? amoxsna. am SemTxvevaSi saZiebeli albaToba iqneba; P( 1.65 N(0,1) 1.65) (1.65) ( 1.65) (1.65) [1 (1.65)] 2 (1.65) 1 20.9505 1 0.9010 . SevniSnavT, rom amoxsnis procedurebi sqematurad gamosaxulia qvemoTmoyvanil sam naxazze: magaliTi 5. vipovoT z -is iseTi mniSvneloba, romlis marjvniv standartuli normaluri ganawilebis wiris qveS moTavsebuli aris farTobi tolia 0.2000-is? amoxsna. cxadia, rom es amocana tolfasia z -is iseTi mniSvnelobis moZebnis, romlis marcxniv normaluri ganawilebis wiris qveS moTavsebuli aris farTobi tolia 1-0.2000=0.8000-is. normaluri ganawilebis cxril- Si vpoulobT 0.8000-sTan yvelaze axlos mdgom ricxvs -- 0.7995-s. es ricxvi dgas 0.8-is Sesabamisi striqonisa da .04-is Sesabamisi svetis gadakveTaze. amitom gasagebia, rom z -is saZiebeli mniSvnelobaa z 0.84 . 72
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omar furTuxia albaToba da statistik
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statistikuri hipoTezis Semowmeba no
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. Tu P( ) aTobebi. P( A): P( ) A
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I. kursze, romelzec sami jgufia, jg
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magaliTi 4. vipovoT albaToba imisa,
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3 10! 8910 С 10 120. 3!7! 6 mag
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C 2 4 6 2 496 C32 0,012 . davaleb
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sa, rom: a). orive nomeri iqneba er
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Tu A ,..., 1 , A2 An xdomilebaTa sr
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1 1 1 1 1 . * * m m1 m 1 m1 sauke
Page 21 and 22: kamaTelze movida kenti qula, C -- o
Page 23 and 24: amocanis pirobebSi cxadia agreTve,
Page 25 and 26: is SemTxvevaSi ukanaskneli Sedegi S
Page 27 and 28: Sesabamisad, saZiebeli albaToba alb
Page 29 and 30: oba aris wina cdaze CaWris albaTobi
Page 31 and 32: 22. ( A B) , P( A| B) 1/3, PA ( )
Page 33 and 34: 42. albaToba imisa, rom oTx damouki
Page 35 and 36: 5). P{ xk} F( xk 0) F( xk ) (Se
Page 37 and 38: E( | B) xiP( xi | B) . 1 cxadia,
Page 39 and 40: { ggg,ggs,gsg,sgg,gss,sgs,ssg, sss}
Page 41 and 42: magaliTi 6. mocemulia SemTxveviTi s
Page 43 and 44: P{ 2} P{ 0} P{ 2} 0.1 0.4
Page 45 and 46: aqedan gamomdinare, korelaciis koef
Page 47 and 48: 17. kompiuteri daprogramebulia 0-da
Page 49 and 50: 37. samSeneblo kompanias sTavazoben
Page 51 and 52: Tavi IV diskretul ganawilebaTa gamo
Page 53 and 54: ualod drois mocemul intervalSi xidz
Page 55 and 56: 9. universitetis studentTa 30%-is a
Page 57 and 58: 27. martis TveSi Semosuli satelefon
Page 59 and 60: 43. umaRlesi ligis fexburTis matCeb
Page 61 and 62: va arcerT kamaTelze, maSin is arafe
Page 63 and 64: 2 2 2 () D x f x dx . asimet
Page 65 and 66: gavixsenoT, rom ( MA) . meore mxri
Page 67 and 68: x amoxsna. visargebloT formuliT: F(
Page 69 and 70: a). ipoveT c ; b). gamoTvaleT moda;
Page 71: Tavi VI normaluri ganawileba SemTxv
Page 75 and 76: X -s Soris mdebare aris farTobi 0.5
Page 77 and 78: amitom 12 a 16a 0.407 da 0.900 .
Page 79 and 80: cali SuSis sawmendidan ramdenis sig
Page 81 and 82: obili 56 mili/sT siCqariT moZraobis
Page 83 and 84: 52. uwyveti SemTxveviTi sididis ga
Page 85 and 86: Tavi VII albaTobis Teoriis zRvariTi
Page 87 and 88: Tu axla gavixsenebT, rom ( x) ( x)
Page 89 and 90: amoxsna. SemoviRoT xdomilebebi: A {
Page 91 and 92: n n 2(0.005 ) 1 0.95, anu ( 0.005 )
Page 93 and 94: 18. detalebis 80% I xarisxisaa. ram
Page 95 and 96: s t a t i s t i k a Tavi I wertilov
Page 97 and 98: ucnobi parametris maqsimaluri dasaj
Page 99 and 100: magaliTi 2. cnobilia, rom garkveuli
Page 101 and 102: ndobis intervali mexuTe klaselebis
Page 103 and 104: tervalisaTvis, roca n 10 ; e). 95%
Page 105 and 106: Tavi II ndobis intervali bernulis s
Page 107 and 108: 4. gamokiTxuli 1015 axalgazrdidan 1
Page 109 and 110: Tavi III ndobis intervali dispersii
Page 111 and 112: 18.6 19.5 20.2 20.4 19.3 21 20.3 19
Page 113 and 114: 26. 22 balaxis sakreWi manqanis mie
Page 115 and 116: Tavi IV 2 hipoTezaTa Semowmeba saSu
Page 117 and 118: xE 43260 42000 z 1.32 . / n 523
Page 119 and 120: 2. CamoayalibeT ZiriTadi da alterna
Page 121 and 122: 15. miuTiTeT unda ukuvagdoT Tu ara
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pasuxebi: 1. 2.58 ; 1.65; -2.58; -
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X E gamoiyene T , T.x. n 1 * ' S
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Seesabameba 0.025 -sa da 0.01 -
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mniSvnelovnebis doniT gvaqvs Tu ara
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gadawyvetileba: Tu T.V.C.R., maSin
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magaliTi 5. vipovoT P -mniSvneloba,
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8. plastikatis boTlSi moTavsebuli 1
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hipoTezis Semowmeba puasonis popula
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3. samSobiaro saxlis warsuli Canawe
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Tavi VIII ndobis intervali da hipoT
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3. uZravi qonebis agentis mtkicebiT
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finansur daxmarebas. imis gasarkvev
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pasuxebi: 1. H0 : E 1800 , H1 : E
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( xn y ) z / n / m a a ( x y )
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P{ T t | H0}, Tu H1 : a1 a2 0; P
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(sadac z aris N(0,1) -is zeda -kr
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amerika evropa 729 329 450 330 481
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TiToeuli jgufidan SemTxveviT SerCeu
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SeniSvna: saSualoTa Sesaxeb tolobis
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gadavideT saSualoebis Sesaxeb hipoT
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4. mkvlevaris SefasebiT studenti go
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Tavi XI oramokrefiani amocanebi pop
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'2 '2 '2 '2 TV . . s1 / s2 246.38
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5. sagadasaxado inspeqtoris mtkiceb
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15. qvemoT moyvanilia A da B tipis
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s n s n ' ' D D d n tn 1, /2 aD d
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s 1 1 1 1 [ d ( d ) ] [4890 (
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4. mkvlevars ainteresebs axali diet
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Tavi XIII oramokrefiani amocanebi b
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( 0.36 0.242, 0.36 0.242) , ( 0.60
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11. 200 gamokiTxuli mozardidan 50-s
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23. dedaqalaqis SemTxveviT SerCeuli
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Tavi XIV Tanxmobis kriteriumebi xi-
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nabiji 4. gadawyvetilebis miReba: r
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e 26.7 55.1 66.64 38.96 12.6 i (aq
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programebs. SemTxveviT SerCeul myid
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nabiji 2. SevadginoT niSanTa SeuRle
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32 29 3235 32 24 e2,1 10.55 , e 8
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nebis doniT, aris Tu ara avtomobili
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hipoTeza imis Sesaxeb, rom arCeuli
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proporcia, romlebic institutSi dadi
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is Sesaxeb, rom im momxmareblebis p
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fatalur avariaTa ricxvi Tavi XVII d
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uaryofi Ti wrfi vi kavSi ri 400 300
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' ' ' 2 x i y i y i yi yi ( yi yi)
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B trestis monacemebi 5. rac ufro ko
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anu y 2.29 x 49.9 . es gantoleba ko
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daskvna. korelaciis koeficientis mi
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218 amocanebi 1. gamoTvaleT korelac
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gacdena, x 10 12 2 0 8 5 Sefaseba,
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Tavi XVIII regresia da korelacia 1.
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wrfiT (regression sum of squares).
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saxlis gayidvis fasi a). ormxrivi a
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2 SSE 21995.88 S 168.91 . n2 13
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determinaciis koeficienti. davweroT
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2 va damakmayofilebel Sedegs (deter
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x1 (b 1 ) 4.146 0.751 5.520 0.000 2
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spirmenis rangobrivi korelaciis koe
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Tavi XIX dispersiuli analizi (ANOVA
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Cven gvaqvs sakmarisi safuZveli dav
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fexburTi kalaTburTi xelburTi ------
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gazze benzinze eleqtronuli meqaniku
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sakredito baraTiT sargeblobisas pro
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pasuxebi: 1. H 0 : a 1 a 2 a 3 , H
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varianti # 2007.1.1 1. Ada B damouk
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( XY , ) (0.5q.); cov(5 X, 4Y 7) (0
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danarTi (statistikuri cxrilebi) k
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1 x N(0.1) -is ganawilebis funqcii
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t (stiudentis) ganawilebis zeda -k
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2 (xi kvadrat) ganawilebis zeda -
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F( n, m ) (fiSeris) ganawilebis zed
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14. studentma unda Caabaros 4 gamoc
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44. saTamaSo kamaTels agoreben samj
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). A -- pirveli agdebisas movida 1
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81. msrolelis mier samiznis daziane
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literatura 1. g. mania. albaTobis T
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