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pasuxebi: 2. 216. 3. a). ara; b). ara. 4. ; . 7. ki. 8. ara. 10. a). A B; b). A B; g). A B; d). A B; e). A B; v). A B; z). A B; T). A; i). ( A B) ; k). B ; l). ( B A) ; m). B . 12. 96. 13. 48. 14. 840. 15. 20. 16. 34. 17. 4200 (sqema 3-3-4: C 3 C 3 ). 10 7 18. 980 (ganTavsebis sqema: 2-2-4 an 2-3-3: C 2 2 2 3 8 C6 C8 C6 ). 19. 35. 20. 56. 21. 56. 22. 512. 24. a). 4/19; b). 9/19; g). 14/19: d). 15/19. 25. a). 1/56; b). 15/56; g). 15/28; d). 5/28. 26. a). 1/21; b). 5/42: g). 5/6 d). 10/21. 27. a). 1/2; b). 3/8; g). 1/8; d). 1/2. 28. a). 1/2; b). 7/16; g). 11/16; d). 15/16. 29. a). 5/16; b). 11/16; g). 15/16; d). 1/16. 30. a). 5/16; b). 5/8; g). 5/8; d). 1/2. 31. a). 15/32; b). 1/2; g). 15/32; d). 15/32. 32. a). 1/2; b). 3/16; g). 15/32; d). 5/16; e). 5/8. 34. 1/6. 35. yvela SemTxvevaSi 11/36. 36. metia pirvel SemTxvevaSi 1/36-iT. 37. orive SemTxvevaSi tolia 1/2-is. 38. a). 1/2; b). 5/9; g). 1/3; d). 1/4; e). 7/36; v). 1/6. 39. orive SemTxvevaSi tolia 1/3-is. 40. metia orjer gagorebisas 1/12-iT. 41. a). 1/9; b). 5/9; g). 5/12; d). 11/36; e). 1/6. 42. a). 1/36; b). 5/9; g). 25/216; d). 1/8; e). 43/216. 43. 91/216. 44. yvela albaToba tolia 91/216-is. 45. 125/216. 46. a). orjer gagorebisas 1/12-iT; b). orjer gagorebisas 5/54-iT; 3). samjer gagorebisas 5/72-iT. 47. a). 1/2; b). 31/72. 50. a). 2/3, 0; b). 1/2, 1/6; g). 5/6, 0; d). 1, 5/9; e). 5/6, 1/4; v). 3/4, 1/3. 51. a). 25/26, 1/18; b). 31/36, 1/6; g). 11/12, 1/9; d). 2/3, 0; e). 4/9, 1/12; v). 7/18, 0. 52. a). 1/3, ara; b). 1/6, ki; g). 1/2, ara; d). 2/5, ara; e). 1/6, ki; v). 1, ara. 53. a). 1/4, 1/4, 1/4, 1/8; b). 1/4, 1/4, 1/4, 1/8; g). 1/8, 1/8, 1/4, 1/16; d). 1/4, 1/8, 1/8, 1/16. 55. a). ki, ki, ara; b). ki, ara, ara; g). ara, ara, ara; d). ara, ki, ki. 57. a). 1/72; b). 1/36; g). 5/108; d). 5/72; e). 7/72; v). 25/216; z). 1/8. 58. 0.986. 60. a). 0.158; b). 0.316; g). 0.526. 61. a). 0.073; b). 0.439; g). 0.488. 62. a). 0.031; b). 0.557; g). 0.412. 63. a). 1/6; b). 1/12. 64. a). 0.06; b). 0.94. 65. a). 0.35; b). 0.65. 66. 66. 0.116. 67. 0.984. 68. 0.518. 69. 0.016. 70. 1/4. 71. 3/8. 72. 11/16. 73. 5/16. 74. 8/27. 75. 11/27. 76. 0.115. 77. 0.853. 78. 0.968. 79. 475. 81. a). 0.06; b). 0.11; g). 0.82; d). 0.87. 82. 0.11; 0.08; 0.92; 0.92; 0.5; 0.08; 0.025. 83. 0.73; 0.46; 0.30; 0.14; 0.04. 84. a). 0.125; b). 0.656; g). 0.986; d). 0.735. 85. a). 1.4-jer; b). 3.4-jer; g). 7.5-jer. 86. 4-jer. 271
literatura 1. g. mania. albaTobis Teoria da maTematikuri statistika. saxelmZRvanelo ekonomikuri fakultetis studentebisaTvis. Tsu, Tbilisi, 1976 2. n. anTelava, a. ediberiZe, g. mania. albaTobis Teoriisa da maTematikuri statistikis amocanaTa krebuli. Tsu, Tbilisi, 1980. 3. mari g., mosiZe a., cigroSvili z., statistika. damxmare saxelmZRvanelo ESM-Tbilisis studentebisaTvis, ESM-Tbilisi, 1996. 4. n. lazrieva, m. mania, g. mari, a. mosiZe, a. toronjaZe, T. toronjaZe, T. ServaSiZe. albaTobis Teoria da maTematikuri statistika ekonomistebisaTvis. fondi «evrazia», Tbilisi, 2000. 5. o. furTuxia. albaTobis Teoria da maTematikuri statistika. Tbilisi, 2007. 6. o.furTuxia. aRweriTi statistika, albaToba, statistikuri daskvnebis Teoria. Tbilisi, 2008. 7. o. furTuxia. albaToba da statistika magaliTebsa da amocanebSi. Tbilisi, 2009. 8. o. furTuxia, z. cigroSvili, q. manjgalaZe. albaToba da maTematikuri statistika. Tsu, Tbilisi, 2009. 9. e. nadaraia, b. doWviri, p. babilua, m. beraZe, g. lominaSvili, m. mnacakaniani. albaTobis Teoris amocanaTa krebuli. quTaisi 2008. 10. e. nadaraia, b. doWviri, T. bokelavaZe, g. lominaSvili, m. mnacakaniani, m. facacia. albaTobis Teoria da maTematikuri statistika (amocanaTa krebuli). quTaisi 2008. 11. Allan G. Bluman. Ementary Statistics: a brief version, second edition. Published by McGraw-Hill, New York, 2003. 12. P. Newbold, W. L. Carlson, B. M. Thorne. Statistics for Business and Economics, sixth edition. Prentice Hall, Upper Saddle River, New Jersey, 2007. 13. В. Феллер. ВВедение в теорию вероятностей и ее приложения. Москва, 1967. 14. УА. Г. Дьячков. Теория вероятностей. Москва, 1980. 15. А. Н. Колмогоров, И. Г. Журбенко, А. В. Прохоров. ВВедение в теорию вероятностей. Москва, 1982. 16. В. К. Захаров, Б. А. Севастьянов, В. П. Чистяков. Теория вероятностей. Москва, 1988. 17. В. Е. Гмурман. Руководство к решению задач по теории вероятностей и математической статистике. Москва, 1988. 272
Page 1 and 2:
omar furTuxia albaToba da statistik
Page 3 and 4:
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
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kamaTelze movida kenti qula, C -- o
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amocanis pirobebSi cxadia agreTve,
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is SemTxvevaSi ukanaskneli Sedegi S
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Sesabamisad, saZiebeli albaToba alb
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oba aris wina cdaze CaWris albaTobi
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22. ( A B) , P( A| B) 1/3, PA ( )
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42. albaToba imisa, rom oTx damouki
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5). P{ xk} F( xk 0) F( xk ) (Se
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E( | B) xiP( xi | B) . 1 cxadia,
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{ ggg,ggs,gsg,sgg,gss,sgs,ssg, sss}
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magaliTi 6. mocemulia SemTxveviTi s
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P{ 2} P{ 0} P{ 2} 0.1 0.4
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aqedan gamomdinare, korelaciis koef
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17. kompiuteri daprogramebulia 0-da
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37. samSeneblo kompanias sTavazoben
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Tavi IV diskretul ganawilebaTa gamo
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ualod drois mocemul intervalSi xidz
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9. universitetis studentTa 30%-is a
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27. martis TveSi Semosuli satelefon
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43. umaRlesi ligis fexburTis matCeb
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va arcerT kamaTelze, maSin is arafe
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2 2 2 () D x f x dx . asimet
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gavixsenoT, rom ( MA) . meore mxri
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x amoxsna. visargebloT formuliT: F(
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a). ipoveT c ; b). gamoTvaleT moda;
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Tavi VI normaluri ganawileba SemTxv
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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
Page 221 and 222: gacdena, x 10 12 2 0 8 5 Sefaseba,
Page 223 and 224: Tavi XVIII regresia da korelacia 1.
Page 225 and 226: wrfiT (regression sum of squares).
Page 227 and 228: saxlis gayidvis fasi a). ormxrivi a
Page 229 and 230: 2 SSE 21995.88 S 168.91 . n2 13
Page 231 and 232: determinaciis koeficienti. davweroT
Page 233 and 234: 2 va damakmayofilebel Sedegs (deter
Page 235 and 236: x1 (b 1 ) 4.146 0.751 5.520 0.000 2
Page 237 and 238: spirmenis rangobrivi korelaciis koe
Page 239 and 240: Tavi XIX dispersiuli analizi (ANOVA
Page 241 and 242: Cven gvaqvs sakmarisi safuZveli dav
Page 243 and 244: fexburTi kalaTburTi xelburTi ------
Page 245 and 246: gazze benzinze eleqtronuli meqaniku
Page 247 and 248: sakredito baraTiT sargeblobisas pro
Page 249 and 250: pasuxebi: 1. H 0 : a 1 a 2 a 3 , H
Page 251 and 252: varianti # 2007.1.1 1. Ada B damouk
Page 253 and 254: ( XY , ) (0.5q.); cov(5 X, 4Y 7) (0
Page 255 and 256: danarTi (statistikuri cxrilebi) k
Page 257 and 258: 1 x N(0.1) -is ganawilebis funqcii
Page 259 and 260: t (stiudentis) ganawilebis zeda -k
Page 261 and 262: 2 (xi kvadrat) ganawilebis zeda -
Page 263 and 264: F( n, m ) (fiSeris) ganawilebis zed
Page 265 and 266: 14. studentma unda Caabaros 4 gamoc
Page 267 and 268: 44. saTamaSo kamaTels agoreben samj
Page 269 and 270: ). A -- pirveli agdebisas movida 1
Page 271: 81. msrolelis mier samiznis daziane
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