А.А. Кудрявцев - Пособие по теории вероятностей (1115312), страница 15
Текст из файла (страница 15)
. . , ξ n¤EÁ Ä ¦Ã aCE  l@E=`!+;$+^ξ(ω) = (ξ (ω), . . . , ξ (ω))n(. - +B='!*)+1B 3HE><A1!*1\'!>'! IR*1LR ''L\HE><1!!$& =E`D N-(;+!>U!'<^< 7'¤EÁ Ħ Ãa CE¯ [ åHE!=E!'<^1nn∈ B},/* AB-)+B=E*^!!*^Ü.B9)P#U ^4P(ξ/ -∈A% *B))-/ 7`=\98:P{ω|--=E'<(ξ%n(ω), 7C98:.!..-;+,$ξ+ (ω))CDP+)"I*.B ∈ BBO^A+)\!'\ø \EH.σIR><1!P#QR =E` ξ ''Ü-9 -"!$& ¼A)+B!' øBHE><1!!$&%Ü\'!><'!ξ , ..., ξ¤EÁĦÃaCE @ !A)+B!!*^)U^-%?-!!$&%x , ..., x0HE!A=E!'<)+^BF!(x'<^L, B..HE.><, x1!)=P#,P(ξ!+;$+n^0EH!E=!'1< x , ..., ξ < x )!'<^QBHE><1!!$&%Q\'!><'! ξ,=E..
`. , ξ ξR ''-9 -"*10HE!=E!'#1GA)+.¤EÁ Ħ Ãa CEä C £H0C5B"'K=EHE*?^UC-><+H)Uø^Q--*% '!!BIE!*^K0HE!=E!'<^f (x) = f (x , . . . , x ) x ∈ IRB∈B1nnnn1n111n111Zf (x) dx ≡nnnnnP(ξ ∈ B) =nnZ...Zf (x1 , . . . , xn ) dx1 . . . dxn ,!$&K -CY*0HE!=E!'<^ +HE6?-2Z¾A*A")+B"!IE6L'!A;+$+)+B!'<^^¾ \/ -HE`><61!"P#]=EAB`$ +.ξ''Q-9 -#!*1QfA(x)*""IE6_BHE><1!!$&%Q\'!><'! ξ , .
. . , ξ RBB1 n!b cWde(fhgiFj® ¤EÁĦÃaC; Ô¢h¾#PD'!!9IE!$& 7'''><"!$& 7'SA)+\!'!.^<A 7*'O!!N;+$+=E6` ^GR A)+\!'<^BHE><1!!$&%\'!><'! ξ C i = 1, . . . , nC=D 7.ξ¾xSaxCE¿!'<^1YIRTFHIOHNPOJ]j\=b k= D& dH&OH&I¾UPIE#WPDNP'!Y!J9I!G=ID v$5h c Q\*Q><"!$0HE{Ç!=EW!_-'!kH'~QH]j\=KHAf[J]r)+K5BFHI .i]PIWRTNP]^JOHIdZbOHYHHQHQG=D&]PFHGHNjm*Nj\*NPOHQK ξ Fi (x) = P(ξi <]j\*x)Njm=bf[iQHRIvG=DstIR-hF (x1 , .
. . , xn )©TFi (xi ) = F (+∞, . . . , +∞, xi , +∞, . . . , +∞).Ö v_:\*I`mD&OHIIFHGHNjm*Nj\*NPOHQHN OHN^sLD&WQH]PQHRT_:V]j\=bk=D&dHOH_:VêWNj\*QHkHQHO-IoW&JIGHQHR»|^JIIFHGHNjm*Nj\*NPOHQHN+QgFHGHQHWNjm*NPR;G.Km¨bJWNPGM5m*NPOHQHdgmH\=KgOHN^sLD&WQH]PQHRT_:V]j\=bk=D&dHOH_:VWNj\*QHkHQHO¤EÁ Ä ¦Ã aC í !+;$+6^¾q|EH<>!1!$]B!'<>!'!$ξ , ..., ξÒ %!"'!>U-=E' Ó D;++''< 7$& 7'UC5-B'Q)U^Q-% B ∈ B C i = 1, . . . , nC1niP(ξ1 ∈ B1 , . . . , ξn ∈ Bn ) = P(ξ1 ∈ B1 ) · . . .
· P(ξn ∈ Bn ).(10.1) [S¾ x axCE 1 :_-GHILM5m*NPOHO=DK+]j\=bk=D&dHO=DK+WNj\*QHkHQHO=D9]^JItVD&]^JQHkHNt]PYHQOHNsLD&WQH]PQJ9I&J\*fcvIdu]j\=bk=D&dHOHIdWNj\*QHkHQHOH_¾x%ÄSxTx1 I]^JGHIQJlXFHI]j\*Njm*IW.DJNj\*lOHI]^J.lXOHNPW_-GHILM5m*NPOHOH_:V5OHN^sLD&WQo]PQHRT_:Vu]j\=bk=D&dHOH_:VWNj\*QHkHQHOÁaCE -cb]^Jl¨v.DstIWINqWNPGHILKJOHI]^JOHIN`FHGHI]^JG=D&OH]jJ.WI¸NP]^JlgJGHIdHYDnUem*N {»RTNPG=DEÃXNPvNPUjD¤FHGHNjm*Nj\*QHRFHI]j\*Njm*IW.DJNj\*lOHI]^Jl]j\=b.o([0, 1], B[0, 1] , λ)λk=D&dHOH_:VuWNj\*QHkHQHO]j\*Njm=bf[iQHRIvG=DstIR-hom ξ1 , ξ 2 , .
. .ξn (ω) =Urm*NAn =n−12[NP]\*QNP]\*Q ω ∈ An ;1,0,ω ∈ An ,2i − 2 2i − 1,,2n2n[ CED9GHQH]^bOHYDV Q QstIvG=DMNPOH_ÇFHNPGHW_-NSm*W.D9k\*NPO=D"|^JIdn = 1, 2, . . .FHI]j\*Njm*IW.DJNj\*lOHI]^J.Qi=1ξ1(ω)10ξ2(ω)1Ïd»¼±º £`í¾ £121ω0Ïd»¼±º £`í¾ ¤1412341ωs jüEt!ý Ú%$Ú¤:« x v²c«SÙ w Æß.ÞàHv²c«ª« w ®ß&®Hv²[ b]^Jl {1FHGHIQstWI\*lOHINO=DJ&bG=D\*lOHIN:kHQH]j\*IHLÄE\=KXFHGHIWNPGHYHQSOHN^sLD&WQH]PQHRTIo]^JQum*QH]PYHGHnN^J.OH_:V)]j\=bk=D&dHOH_:V+WNj\*QHkHQHOum*I]^J&DJIkHOHI"FHIYDsLDJl9]PFHG=D&WNjmH\*QHWI]^JlG=D&WNPOH]^JW.D`Ó [JI\*lYIymH\=K W]PNjV Itm*OHI&JIkHNPkHOH_:V`RTOHILMNP]^JW]PR-Bi = {xi }GHN^pNPOHQHNXstDmDkHQ+ j=k=D&]^JOHI]^JQnHmH\=KQHRTNPNPR[x1 = .
. . = x n = 1P(ξ1 = 1, . . . , ξn = 1) = P10, n2=1= P(ξ1 = 1) · . . . · P(ξn = 1).2n¤kHNPWQm*OHIHn=kJImH\=KyI]^JD\*lOH_:VG=D&WNPOH]^JWI5J&D&YMNW_-FHI\*OKHN^J]Kx1 , . . . , x n ¤Á ux YHGHQJNPGHQHd OHN^sLD&WQH]PQHRTI]^JQ* j@ D;++''< 7$nPD)'¾`IE=PD)C=PD )|q'<%¾HE-><91! !-$"!*B^M'!0><HE'!!!=E$ .ξ , ..., ξ!!'<'!^V1(AA)+)B\!!'<'<^G^QA)U^O)+"-% +'< 7V+'!)+A*'U ;)+#!'<^ 7#PD'!!9IE!$&%,0HE!=E.x , .
. . , x ∈ IR1n1nF (x1 , . . . , xn ) = F1 (x1 ) · . . . · Fn (xn ).hçà Äç:[ } T]j\*QgG=D&]PFHGHNjm*Nj\*NPOHQHN]j\=bk=D&dHOHIU^IWNPYJIG=DKHW\=KHN^J]KD&v]PI\*f[JOHIOHNPFHGHNPGH_-WOH_-R-n:JI`OHNPIvtV.ILm*QHRT_-RÀQ§m*Iξ]^J&=DJ(ξIk1o ,. .
. , ξn )OH_-Rb]j\*IWQHNPRÇOHN^sLD&WQH]PQHRTI]^JQKHW\=KHN^J]rKWI&stRTIM9OHI]^Jl+FHGHNjm*]^JD&Woξ1 , . . . , ξ n\*NPOHQK`mH\=KgW]PNjV]PI&WRTNP]^JOHId¨F\*I&JOHI]^JQ¨YD&Y§FHGHIQstWNjm*NPOHQKx1 , . . . , xn ∈ IR=h 7#PD'!!9IE!$&%MA*"1f (x1 , . . . , xn ) = f1 (x1 ) · . .
. · fn (xn ). b]^JlQ{ OHN^sLD&WQH]PQHRT_-N)]j\=bk=D&dHOH_NqWNj\*QHkHQHOH_¼]ZbOHYHHQKHRTQG=D&]joξ ηFHGHNjm*Nj\*NPOHQKQ]PII&JWN^J]^JWNtOHOHIHHCED&dm*NPRZbOHYHHQHf¯G=D&]PFHGHNjm*Nj\*NPOHQHKH(x) G(x)]^bRTRT_1|^JQVu]j\=bk=D&dHOH_:VWNj\*QHkHQHOI5IvIv&iNPOHOHIduZEIGHR¦bt\*NXFHI\*OHIduW&NPGHIKJoOHI]^JQQHRTNPNPRF (x) = P(ξ + η < x) = P(ξ < x − η) =+∞Z−∞H(x − y) dG(y).¾D&RTN^JQHR-n=kJImD&OHO=DKuZEIGHR¦bt\DKHW\=KHN^J]rK]PQHRTRTN^JGHQHkHOHIdn*JIzNP]^JlF (x) =+∞ZG(x − y) dH(y).!;+¤$+EÁ Ä^M¦ 0ÃHEa !CE=E!'<¯ ^ Ô0|0B"=*1M0HE!=E!'!1A)+\!'<^−∞F (x) =+∞Z−∞H(x − y) dG(y) =+∞Z−∞G(x − y) dH(y).H(x)'G(x)b!cWde(fhgiFj® @ / -;+!>U!'9 F (x) = (H ∗ G)(x) = (G ∗ H)(x) '' F = H ∗ G = G ∗ H R¾xSaxCE¨ @ ¡SbOHYHHQK"G=D&]PFHGHNjm*Nj\*NPOHQK"]^bRTRT_¨m*W&b.VzOHN^sLD&WQH]PQHRT_:V]j\=bk=D&dHOH_:VWNj\*QHkHQHONP]^Jlz]PWNPGJYD5ZbOHYHHQHdG=D&]PFHGHNjm*Nj\*NPOHQHK]j\D&UjD&NPRT_:V¾xSaxCE¼ £HT]j\*QZbOHYHHQKG=D&]PFHGHNjm*Nj\*NPOHQKQHRTNPN^JgF\*I&JoH(x)OHI]^JlnJIz]PWNPGJYDJD&YM5NQHRTNPN^J"F\*I&JOHI]^JlF (x) = (H ∗ G)(x)h(x)f (x) =+∞Zh(x − y) dG(y).(10.2)AA*¤)+\!EÁ!* 1Ü'<Ä^ 0¦ HEÃ!a=E!C'!"'1 =E* ^U C5A Ö><0)+å\ HE!!=E'<!^'<^(F(x)A+CR -)+B\'4!HE'<?^ -H(x)+H!¶;+$0+HE!=E!'<^¾^=D 7..G(x)F =G∗H¤EÁĦÃaC &|h'< @ 'U;+!'1S0HE!=E!'!'"A)+\!'<^F (x)!;+$+^Q0HE!=E!'<^(A)+B!'<^−∞FS(s)(x) =+∞ZF (x + y) dF (y).−∞¾ x axCE Ô¢ç:QHRTRTN^JGHQsD&HQK5ZbOHYHHQHQG=D&]PFHGHNjm*Nj\*NPO=QKNP]^JlF (x)ZbOHYHHQKG=D&]PFHGHNjm*Nj\*NPOHQKÇG=DstOHI]^JQOHN^sLD&WQH]PQHRT_:VItm*QHO=D&YIWI¸G=D&]PFHGHNjm*Nj\*NPOoOH_:Vu]j\=bk=D&dHOH_:VWNj\*QHkHQHOn=QHRTNPf[iQVZbOHYHHQHfÇG=D&]PFHGHNjm*Nj\*NPO=QKF (x)¾x axCE ç:QHRTRTN^JGHQHsLD&HQKyZbOHYHHQHQ'G=D&]PFHGHNjm*Nj\*NPOHQK'KHW\=KHN^J]rKZbOHYHHQHNPdzG=D&]PFHGHNjm*Nj\*NPO=QKz]j\=bk=D&dHOHIdzWNj\*QHkHQHOH_ nQHRTNPf[iNPdη^nHJI9N^]^JlS A)+\!'S'< @ '!><P(η < x) = P(η > x)mH\=K9W]PNjV&ÄSNPdH]^JWQJ.Nj\*lOHIHnFb.]^JlnUem*N Q{¥OHN^sLD&WQH]PQHRT_-Ndx ∈ IRη = ξ − ξ1ξ ξ1ILm*QHO=D&YIWI5G=D&]PFHGHNjm*Nj\*NPOHOH_%NS]j\=bk=D&dHOH_-NXWNj\*QHkHQHOH_*IUemD[P(η < x) = P(ξ − ξ1 < x) = P(ξ1 − ξ < x) = P(−η < x) = P(η > x).¾x%ÄSxTxä b]^Jl Q { OHN^sLD&WQH]PQHRT_-N]j\=bk=D&dHOH_-NWNj\*QHkHQOH_nQHRTNjof iQHNG=D&WOHIRTNPGHOHINO=D9I&JGHξN^stYηN[G=D&]PFHGHNjm*Nj\*NPOHQHNCED&dJQ)G=D&]PFHGHNjm*Nj\*NPO=QHN[0, 1]]j\=bk=D&dHOHIdWNj\*QHkHQHOH_ξ+ηÁaCE -.b.]^Jl{ÇF\*I&JOHI]^JlX]j\=bk=D&dHOH_:V5WNj\*QHkHQHO Q CED&dm*NPRh(x)ξ ηF\*I&JOHI]^Jl]j\=bk=D&dHOHIdWN\*QHkHQHOH_*¾D&RTN^JQHR-n=kJIom f (x)ξ+ηh(x − y) =10h(y) =10FHGHQFHGHQ x − y ∈ [0, 1];x − y 6∈ [0, 1],FHGHQFHGHQ y ∈ [0, 1];y 6∈ [0, 1].s jüEt!ý Ú%$Ú¤:« x v²c«SÙ w Æß.ÞàHv²c«ª« w ®ß&®Hv²:I]PFHI\*l&sPbNPRT]rKZEIGHR¦bL\*Id`Ó [ j=RTNPNPR £f (x) =+∞Z−∞h(x − y)h(y) dy. GHQFHItm*_-OJNPUPG=D\*lO=DKZbOHYHHQKqG=D&WOKHN^J]K Obt\*fSGHQx 6∈ [0, 2]FHItm*_-OJNPUPG*D\*lO=DK9ZbOHYHHQK9G=D&WOKHN^J]rK9Njm*QHOHQHHN[JIUemDXQ5JI\*lYIXJIUexmD∈nY[0,IUrm2]DQ FHGHQHO=DmH\*N^M5DJ5I&JGHN^stYbItm*OHIWGHNPRTNPOHOHIHnHJI5NP]^Jlx−y y[0, 1]x−1 ≤ y ≤ x¦D&YHQHRgIvG=DstIR-nHFHGHQx ∈ [0, 1]f (x) =Zx0DFHGHQx ∈ [1, 2]f (x) =Z1x−1h(x − y)h(y) dy = x,h(x − y)h(y) dy = 2 − x.I]^J&D\*lOH_:VyJIkHYDVf (x) = 0Ö RT_ÂFHI&stO=D&YIRTQ\*QH]Pl]yFHIOKJQKHRTQ§YIW.D&GHQ=D&HQK'QYI|PZEZEQHHQHN^OJYIGHGHNj\=KHHQHQ=ÁD&]P]PRTI&JGHQHR¨OHNPYI&JIGH_-NE]PWIdH]^JW.D|^JQVyIv&¹NPYJIWH=u_bMNFHIoYDsLD\*Qn=kJI9N^]j\*Q]j\=bk=D&dHOH_-NSWNj\*QHkHQHOH_¯KHW\=KHf[J]rKuOHN^sLD&WQH]PQHRT_-RTQn*JIzQVyYIoW.D&GHQ=D&HQKyG=D&WOKHN^J]rKObL\*fS*:NPGHOHI\*QuIvG=DJOHINbJWNPG.M5m*NPOHQHNLw¾x%ÄSxaxû @ IYDsLDJlHnkJI+Qs'OHNPYIGHGHNj\*QHGHIW.D&OHOHI]^JQ§]j\=bk=D&dHOH_:VWNjo\*QHkHQHO Q OHNE]j\*Njm=bN^Jn*kJI Q OHN^sLD&WQH]PQHRT_ξ ηξ ηÁaCE -*b.]^Jl Q {äOHN^sLD&WQH]PQHRT_-NE]j\=bk=D&dHOH_-NXWNj\*QHkHQHOH_n=FHGHQHkHNPRTI\*ILM9QHR ζ ξT¤kHNPWQm*OHIHnTkJIQOHN"KHW\=KHf[J]K§OHN^sLDoEξ = Eζ = 0= ξζWQH]PQHRT_-RTQ sLDqQH]PY\*fckHNPOHQHηNtR»JGHQHWQ=D\*l&OH_:V¸]j\=bk=DNPξWHnO=ηD&FHGHQHRTNPGnaYIUrmD{ξW_-GHILM5m*NPOHO=DKu]j\=bk=D&dHO=DKuWNj\*QHkHQHO=D. j*GHQu|^JIR Tom Eξη = Eξ 2 ζ = Eξ 2 Eζ = 0 = EξEη.¾ x%ÄSxaxÀ £H*IYDsLDJlnkJI9YI|PZEZEQHHQHNPOJ'YIGHGHNj\=KHHQHQ\*fcv_Vρ(ξ, η)OHNPW_-GHILM5m*NPOHOH_:V9]j\=bk=D&dHOH_:V"WNj\*QHkHQHO Q nQHRTNPf%iQV"YIOHNPkHOH_-NcW&JIGH_-NcRTIoξ ηRTNPOJ_n*Iv\DmD&N^Jz]PWIdH]^JW.D&RTQh [ @ ρ(ξ, η) = 0nHNP]j\*Q|ρ(ξ, η)| ≤ 1|ρ(ξ, η)| = 1]PW&KsLD&OH_ξQηOHN^sLD&WQH]PQHRT_~~JIUemDcQXJI\*lYI[JIUrmDnYIUemDξQηFHIkJQO=D&WNPGHOHINT\*QHOHNPdHOHIb!cWde(fhgiFj®omaCE-NPGHWINE]PWIdH]^JWIzv_:\*IzIv&I]POHIW.D&OHI5WGTÁξ − Eξξ1 = √DξQ ¢Ö *b]^Jlη − Eηη1 = √.Dη¾ D&RTN^JQHR-nkJIQ]j\=bk=D&dHOH_-N5WNj\*QHkHQHOH_nbtm*IoEξ1 = Eη1 = 0 Dξ1 = Dη1 = 1W\*N^JWIG.K=f%iQHNE|^JQHR§]PWIdH]^JW.D&R§O=Dst_-W.D&f[J]rK5QX]PIIJWN^J]^J.WNPO=OHI jç:FHG=D&WNjmH\*QHW.DE]j\*Njm=bf[iDK9HNPFHI&kHYD]PII&JOHI&pNPOHQHdhQ!'*+!!$& 7' ¾`E 7'*.+!!$& 7'0 ≤ D(ξ1 ± η1 ) = E(ξ1 ± η1 )2 = Eξ12 + Eη12 ± 2ρ(ξ, η) = 2 ± 2ρ(ξ, η),YI&JIG=DKyQ'm*IYDst_-W.D&N^J9W&JIGHINE]PWIdH]^JWIzYI|PZEZEQHHQHNPOJDzYIGHGHNj\=KHHQHQb]^Jl Q FHIkJQ'O=D&WNPGHOHIN[\*QHOHNPdHOHI]PW&KsLD&OH_nJINP]^JlmH\=KuOHNPYI&JIξ GH_:ηVym*NPdH]^JWQJN^\*lOH_:VkHQH]PNj\ Q=RTNPNPR P(η = a + bξ) = 1ab 6= 0ò`ó ô b.´µξ − Eξ a + bξ − a − bEξ√ρ(ξ, η) = E √·=Dξ|b| DξGHNjm*FHI\*ILM9QHRgJNPFHNPGHlHn*kJI|ρ(ξ, η)| = 1HIUemDD(ξ1 ± η1 ) = 2 ± 2ρ(ξ, η) = 0.C IgFHI]j\*Njm*OHNPNG=D&WNPOH]^JWI¨RTILM5N^JgQHRTN^Jl¨RTNP]^JIg\*QplgWg]j\=bk=D&N&n[YIUemDg]j\=b.ok=D&dHO=DKWNj\*QHkHQHO=DKHW\=KHN^J]rKêW_-GHILM5m*NPOHOHId¥W§OHNPYI&JIGHIdJIkHYN jξ1 ± η 1cça\*Njm*IW.DJNj\*lOHIHn!√√qDξDξP ξ = ∓ √ η ± √ Eη + c Dξ + Eξ = 1.DηDηM5~_7 77[¾x%ÄSxTxÀ Ô¢*IYDsLDJlz]^FHG=D&WNjmH\*QHWI]^Jl9sLD&RTNPk=D&OHQK ¾x%ÄSxTx¯ I]^JGHIQJlFHI]j\*Njm*IW.DJNj\*lOHI]^J.lOHN^sLD&WQH]PQHRT_:V]j\=bk=D&dHOH_:VWNj\*QHkHQHOn*QHRTNPf[iQVuG=D&WOHIRTNPGHOHINEO=D5I&JGHN^stYNG=D&]PFHGHNjm*Nj\*NPOHQHN[0, 1]¾x%ÄSxTxä Ôb]^Jl Q { OHN^sLD&WQH]PQHRT_-N]j\=bk=D&dHOH_-NWNj\*QHkHQOH_nQHRTNjof[iQHN[G=D&WOHIRTNPGHOHIN%O=DI&JGHξN^stYN ηG=D&]PFHGHNjm*Nj\*NPO=QHN&CED&dJQz]PQHRTRaNjJGHQHsLD&HQHf[0, 1]QVuZbOHYHHQHQG=D&]PFHGHNjm*Nj\*NPOHQHK¾x%ÄSxTxÅ Ö TuIU^bJ+\*Q§OHNPW_-GHILM5m*NPOHOH_-Ny]\=bk=D&dHOH_-NuWNj\*QHkHQHOH_Qξ ηv_JlS]^JItVD&]^JQ=kHNP]tYHQ9OHN^sLD&WQH]PQHRT_-RTQnNP]j\*QzIOHQz]PW&KsLD&OH_¨ZbOHYHHQHIO=D\*lOHIdzsLDoWQH]PQHRTI]^JlfSn*O=D&FHGHQHRTNPGn 2w2ξ +η =1s jüEt!ý Ú%$Ú¤:« x v²c«SÙ w Æß.ÞàHv²c«ª« w ®ß&®Hv² ¾x%ÄSxax b]^Jl Q{û]j\=bk=DdHOH_-NzWNj\*QHkHQHOH_nξ ηnÄSIYDsLDJlHn=kJI Q OHNEOHN^sLD&P(ξWQH]PQH>RT_0) = P(η >0) = 3/4 P(ξ + η > 0) = 1/2ξ η¾x%ÄSxax Eça\=bk=D&dHOH_-NgWNj\*QHkHQHOH_QOHN^sLD&WQH]PQHRT_ Q¿QHRTNPf%Jξ1ξ2Fb.D&]P]PIOHIW]PYINSG=D&]PFHGHNjm*Nj\*NPOHQ=NS]XF=D&G=D&RTN^JG=D&RTQQ]PI&I&JWN^J]^J.WNPO=OHIHnFHGHQoλ1 λ2kHNPRÄSI&YDsLDJlHn¦kJI+mH\=K\*f[vIUPIW_-FHI\*OKHN^J]rKgOHNPG=D&WNPOH]^JWIλ1 ≤ λ 2t ≥ 0P(ξ1 ≤ t) ≥ P(ξ2 ≤ t)¾x%ÄSxaxê &ça\=bk=D&dHOH_-NWNj\*QHkHQHOH_QOHN^sLD&WQH]PQHRT_§QQHRTNPf%JFbD&]joξ1 ξ2]PIOHIW]PYINqG=D&]^FHGHNjm*Nj\*NtOHQHN ]qF=D&G=D&RTN^JG=DRaQQ]PII&JWN^J]^J.WNPOHOHIH[CED&dJQλ1λ2nP(ξ1 = k| ξ1 + ξ2 = n) k = 1, .
![](https://s.studizba.com/z.php?f=/templates/si/i/noavatar.png&w=100&h=100&t=1"){kind=avatar}
