Tsu-2011 - ieeetsu

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vigulisxmoT, rom im SemTxvevaSi, roca testireba utardeba adamians, romelsac ara aqvs avadmyofoba, maSin 1%-ia albaToba imisa, rom miviRoT mcdari dadebiTi Sedegi, e.i. P ( dadebiTi| janmrTeli ) 1% da P ( uaryofiTi| janmrTeli ) 99% . dabolos, davuSvaT, rom im SemTxvevaSi, roca testireba utardeba avadmyof adamians, maSin 1%-ia albaToba imisa, rom miviRoT mcdari uaryofiTi Sedegi, e.i. P ( uaryofiTi| avadmyofi ) 1% da P ( dadebiTi| avadmyofi ) 99% . gamoTvaleT albaToba imisa, rom: a). adamiani janmrTelia, xolo testma aCvena uaryofiTi Sedegi; b). adamiani avadmyofia, xolo testma aCvena dadebiTi Sedegi; g). adamiani janmrTelia, xolo testma aCvena dadebiTi Sedegi; g). adamiani avadmyofia, xolo testma aCvena uaryofiTi Sedegi. ganvixiloT realuri situacia, romelic gviCvenebs erTi SexedviT moulodnel gansxvavebas P ( A| B) da P ( B | A) pirobiT albaTobebs Soris. imisaTvis, rom gamovavlinoT seriozuli avadmyofobis mqone adamianebi adreul stadiaze, xdeba adamianebis didi jgufis testireba. miuxedavad winaswari Semowmebis sargeblobisa, am midgomas gaaCnia uaryofiTi mxare: Tu adamians sinamdvileSi ar gaaCnia avadmyofoba da sawyisma testma aCvena dadebiTi Sedegi (daudgina avadmyofoba), is iqneba stresul mdgomareobaSi (rac Tavis mxriv uaryofiTad moqmedebs mis cxovrebaze) sanam ufro warmatebuli testi ar aCvenebs, rom is janmrTelia. am problemis mni- Svneloba SesaZlebelia kargad gavigoT pirobiTi albaTobebis termineb- Si. wina davalebis monacemebSi gamovTvaloT albaToba imisa, rom testi aCvenebs dadebiT Sedegs. sruli albaTobis formulis Tanaxmad: P( dadebiTi ) P ( janmrTeliP ) ( dadebiTi| janmrTeli ) P( avadmyofi ) P( dadebiTi| avadmyofi ) 0.99 0.01 0.01 0.99 0.0198 . rogorc cnobilia, magaliTis pirobebSi P ( dadebiTi| avadmyofi ) 99% . gamovTvaloT axla Sebrunebuli pirobiTi albaToba, risTvisac visargebloT pirobiTi albaTobis ganmartebiTa da namravlis albaTobis formulebiT. maSin zemoT miRebuli P( dadebiTi ) 0.0198 1.98% Sedegis Tanaxmad: P( avadmyofi dadebiTi) P( avadmyofi| dadebiTi) PPP(dadebiTi) P( avadmyofi)P P( dadebiTi | avadmyofi ) 1% 99% 50% . PP1.98% 1.98% rogorc vxedavT, pirobiTi albaToba imisa rom testi mogvcems dadebiT Sedegs, pirobaSi rom adamiani avadmyofia tolia 99%-is, maSin rodesac pirobiTi albaToba imisa rom adamiani avadmyofia, pirobaSi rom testma mogvca dadebiTi Sedegi aris mxolod 50%. aq SerCeuli monacemeb- 23
is SemTxvevaSi ukanaskneli Sedegi SeiZleba CaiTvalos miuRebelad: naxevari adamianebis, romelTa testirebam aCvena dadebiTi Sedegi, faqtiurad aris janmrTeli. magaliTi 12. yuTSi moTavsebulia ori moneta: A 1 -- simetriuli moneta gerbis mosvlis albaTobiT 1/2, da A 2 -- arasimetriuli moneta gerbis mosvlis albaTobiT 1/3. SemTxveviT viRebT erT monetas da vagdebT. davu- SvaT, rom movida gerbi. rogoria albaToba imisa, rom amoRebuli moneta iyo simetriuli? amoxsna. am SemTxvevaSi elementarul xdomilebaTa sivrce iqneba: {( A1 , g),( A1 , s),( A2 . g),( A2 , s)} , sadac magaliTad, ( A 1 , g) -- niSnavs, rom amoviReT A 1 moneta da misi agdebis Sedegad movida gerbi. amocanis pirobebSi gvaqvs: P ( A1 ) P( A2 ) 1/2, P ( g | A1 ) 1/ 2 da P( g | A2 ) 1/ 3. Sesabamisad, namravlis albaTobis formulis gamoyenebiT gamoviTvliT: P {( A 1 , g)} 1/ 4, P {( A 1 , s)} 1/ 4, P {( A 2 , g)} 1/ 6 da P {( A 2 , s)} 1/ 3. amitom baiesis formulis Tanaxmad P( A1 ) P( g | A1 ) 3 P( A1 | g ) . P( A1 ) P( g | A1 ) P( A2 ) P( g | A2 ) 5 cxadia, agreTve rom P ( A 2 | g) 2/ 5. magaliTi 13 (keTil gamomcdelze I). vTqvaT, Cven Casabarebeli gvaqvs gamocda da SegviZlia avirCioT nebismieri sami gamomcdelidan. davuSvaT, CvenTvis cnobilia, rom erTerTi sami gamomcdelidan (ucnobia romeli) -- “keTilia” da albaToba imisa, rom masTan Caabaro gamocda tolia 0.4-is, xolo danarCeni ori gamomcdeli “avia” da maTTan gamocdis Cabarebis albaToba tolia 0.1-is. Cven SemTxveviT avirCieT gamomcdeli da warmatebiT CavabareT gamocda. rogoria labaToba imisa, rom Cven avirCieT “keTili” gamomcdeli? amoxsna. SemoviRoT Semdegi xdomilebebi: A -- amorCeuli gamomcdeli “keTilia” (maSin A -- iqneba xdomileba, rom amorCeuli gamomcdeli “avia”) da B -- gamocda Cabarebulia (Sesabamisad, B -- gamocda araa Cabarebuli). amocanis pirobebSi gvaqvs: P ( A) 1/3, P ( A) 1 P( A) 2/ 3; P( B| A) 0.4 , P( B| A) 1 P( B| A) 0.6 ; P( B| A) 0.1 , P( B| A) 1 P( B| A) 0.9 . cnobilia, rom moxda B xdomileba da gamosaTvlelia pirobiTi albaToba P ( A| B) . vinaidan, A da A xdomilebebi qmnian srul sistemas, baiesis formulis Tanaxmad saZiebeli albaToba iqneba: P( A) P( B | A) 2 P ( A| B) . P( A) P( B | A) P( A) P( B | A) 3 24
Page 1 and 2: omar furTuxia albaToba da statistik
Page 3 and 4: statistikuri hipoTezis Semowmeba no
Page 5 and 6: . Tu P( ) aTobebi. P( A): P( ) A
Page 7 and 8: I. kursze, romelzec sami jgufia, jg
Page 9 and 10: magaliTi 4. vipovoT albaToba imisa,
Page 11 and 12: 3 10! 8910 С 10 120. 3!7! 6 mag
Page 13 and 14: C 2 4 6 2 496 C32 0,012 . davaleb
Page 15 and 16: sa, rom: a). orive nomeri iqneba er
Page 17 and 18: Tu A ,..., 1 , A2 An xdomilebaTa sr
Page 19 and 20: 1 1 1 1 1 . * * m m1 m 1 m1 sauke
Page 21 and 22: kamaTelze movida kenti qula, C -- o
Page 23: amocanis pirobebSi cxadia agreTve,
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 and 72: Tavi VI normaluri ganawileba SemTxv
Page 73 and 74: magaliTi 4. vipovoT albaToba imisa,
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X -s Soris mdebare aris farTobi 0.5
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amitom 12 a 16a 0.407 da 0.900 .
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cali SuSis sawmendidan ramdenis sig
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obili 56 mili/sT siCqariT moZraobis
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52. uwyveti SemTxveviTi sididis ga
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Tavi VII albaTobis Teoriis zRvariTi
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Tu axla gavixsenebT, rom ( x) ( x)
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amoxsna. SemoviRoT xdomilebebi: A {
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n n 2(0.005 ) 1 0.95, anu ( 0.005 )
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18. detalebis 80% I xarisxisaa. ram
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s t a t i s t i k a Tavi I wertilov
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ucnobi parametris maqsimaluri dasaj
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magaliTi 2. cnobilia, rom garkveuli
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ndobis intervali mexuTe klaselebis
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tervalisaTvis, roca n 10 ; e). 95%
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Tavi II ndobis intervali bernulis s
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4. gamokiTxuli 1015 axalgazrdidan 1
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Tavi III ndobis intervali dispersii
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18.6 19.5 20.2 20.4 19.3 21 20.3 19
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26. 22 balaxis sakreWi manqanis mie
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Tavi IV 2 hipoTezaTa Semowmeba saSu
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xE 43260 42000 z 1.32 . / n 523
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2. CamoayalibeT ZiriTadi da alterna
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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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