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PithStat2005 - ZXOAH HM&MY Iavom‘ipwg 2005 EEAMHNO...

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Unformatted text preview: ZXOAH: HM&MY Iavom‘ipwg 2005 EEAMHNO: 3° GEQPIA HIGANOTHTQN KAI ETATIETIKH @EMA 1: A) ’Evag naixmg naiga éva wxepé' gram/{51 N (pepég, 67:01) N given 1.1.1. 7:01) alcolnvfiei mv Kawvom Poisson pa napc‘ipzs’cpo X. 25 K003 enmfilnwn 1:01) mam/151013 n mfiwémm vu Kapfiioat eivm p 1cm. 1] n10avémw v0. XtiGEI eivcu q =1-p. Ecru) X o "ap10 06g ’50))! nmxwfitc’bv non Képfiwa Km Y 0 (11310 06g TOJV natxwfildw 7:01) éxacse. Na DROMYIGTOBV 01. mpmccirw m0avémtsg: i)P[X=j], P[Y=k] Kat P[X=j,Y=k], 1.13 j=0,1,... Km. k= 0,1,... ii) Na séewmei cw 01 m. X, Y eivm avagdpmreg. B) Av B1, B2, eivw. pint apteufimun axokoveia gévcov svfiexouévmv 1:01) 581.700.104.100 xéapou 9, pa UjBi = Q Km. P(Bi) > 0 (i = 1,2,...)1615 VOL Satxtai 611 710. was evéexépevo AIGxOEII P(A) =2, P(AlBi)P(Bi). @EMA 2: A) H fitdpmw. Cwfig X as cbpsg svég mzm'AMK'ctKofi mag unxavfig six/m ”L. us amt. 1 1 f =-———- -—--- -—50 >50. (X) 40 exp{ 40 (x )}, 2: How 11 mam/6mm (ho-Is n latrovpyia mg pnxavfig W. m gamma-:1 mg 5000 éapsg, ow 51a0érovue cvvokmi 60 155.10th awaflaxnxd; B) Ta. avfiexépeva A, B aivm magapmw pa avricsrmxag memémreg P(A) = a, P(B) == [3. Na Bpefiei T] meavémm va Guuflai éva uévo (111:0 m svéaxéuava A, B. @EMA 3: A) ”E0103 X 1'41. [48 (mun. ‘f(X)=-—-1—BXP(*-1-X2), xeR. J52? 2 Na fipafiei T] can. mg 1:. u. Y= ex. B) 'Ecnm X, Y wegdpmteg 1:41.. us Icon/1'1 Emmopét C52. @é'rovua U = 3X - 2Y Km W = 5X + 4Y. Na. Bpeeei o wwskeorfig coaxénong pCU, W). @EMA 4: ”Es—cm Tuxedo 530mm X1, . . .,Xn (m6 mv‘ onetéuopqm Kamvoufi cw 5100mpa[10, l3], |3>10. i) Na. Bpsfiei n exnufitpux mu [3 He mv ”£0050 TEDV poncbv. ii) Nu. Bpaeei 11 EMII. mu B 1cm. 1] 0.7m. cwmg. iii) Egatdc'ra 0w 1mm (13:6 1.1g napumivm given. auspéknnm sxnufirpta mg napapétpon [3. @EMA 5: A) H eatifioon 10 ”(1011er mag Icigng A Ken. 11 uaflnrcbv mag Mug tdgng B :33 Kdamw mien pa Six/amt (m6 10v napaxdtm xivaxa: mm- m i) Na 5003i éva 0.90 — AE. 1501) M701) TCDV fitaczrcopdw mg 2 mafia; ii) M3 [3am] TO npdyco epo’hm p.11 v11 agemcstei av 01. uécseg amfiéaexg 103v ”(10111:de cmg 5130 Idgatg aivm {flag as 8.6. a = 0.01.. B) 28 npoxawpwcé wxaio 53%pr payéBong 50 nohtcbv Bpéfinxav 28 01 (moim fiwv unép mag nolmxfig Bécmg. M3 1361.011 mv napandvco nlnpo¢0pia m Bpeeei TO alanmo pé'yafiog TOD Baiyua'rog 11 (bars p.23 memémm rovmxtmov 095 1:0 anélvto cmdkua amipncmg I}; - pl v0. aivat pucpétepo 101) 0.05. * Na draw-titers 0'3 4 arm to: 5 fiéyara, éva rovléxm'mv and K0268 zapwxfi. * ** BAQMOAOP IA A: 1. 7,, B: 0.3 ** 9"” Alépxsm Eééraang: 2 ’A: h *** _ ...,Xn (m6 Kawvoufi 113 5.17:. f(x)= RX.“ , 0 < x < 1 A > O. Na. Bpaeai n akuufitpta 1:01) 3. pa mv “£28050 103v pono’bv. @EQPIA HIGANOTHTQN KAI ZTATIZITIKH A) Mia. KW naptéxat 5 Xavkég Km 4 uafipag cscpaipag. Haipvovpa wxaia “it: mpaipa m1 av given lavKfi mv LiavaBdCovua uéca uaCi pa (mug 3 Aavkég, gvci) 0w given um} p11 mv éavaBéCova uécm. put]: us dlkg 2‘ uaflpag. Na umkoytmofiv 01. napmcdw xtemérntag: - i) Na six/(11 lama) cm] 5313mm Mum. ii) Na Sivan. land] cmv arpcbrn lfiwn, éafiouévov 6n six/(11. 1.30mi va Sabrepn Mum. B) 'Emm X, Y fitmcprrég 1cm avafitipmtag 13.1.1. i) Aaiire 61:1 E[g(X) h(Y)] = E[g(X)] E[h(Y)], 61:01) g, h svvaprficag 7m 1m; onoiag ii) Av 01. X, Y axolovGOfw rm: Katampfi Poisson pa napdue'cpo 1. V0. mmkoywrai n E[exp(X - Y)]. A) H Stdplcgm Cmfig T (h) avég afiap‘rfiua‘zog aivm 144. pa 5.1.2:. £0) = 39.11:3 exp(—6t3), t> 0 -I B) 'Emco mxaio 55:1.th X1,,.,....,X1n cataté Katcwoufi pa 01mm f(x) = OL+1)X'L2 , x > 1,, 9L > 0. Non Bpaeai n axnpfirpta 1:01) A us 11112 ”$8050 row pondw. A) @alficaua va. Guyxpivovua 1:0 pécso Kémog Staépombv pa raéi omv ABfiva Km GIT] Mafipim. ®3wpofiua (31:1 w. awimmxa Kécn'n aivou 1:41. us mmvouég 71a mv Aefiva X1 ~N(,u].012) 1cm 71a 1:1] Maépirn X2 --— N (#3032). A130 comic: Seiyuaw ueyéeong 111 = 16 m1. 112 = 13 71a Aefiva 1cm Maépim awictmxa éémoav 3?; = 3 .936 , 51 = 0.787 6 _., 3'62 24.42 € 1cm. 52 = 0.92 6. Na 5093i éva 0.98 - AE. 1:01) Myov of RI; raw Stagnopc'ov. *BAQMOAOFM A: 1.. 7,, B: 0.8 * “Aw’éplcam Eféz'acqg: 2 ‘96 h ** EICXOMdETE EHITYXlA ...
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