А.А. Кудрявцев - Пособие по теории вероятностей (1115312), страница 2
Текст из файла (страница 2)
. .OHIduW&Nj\*QHkHQHOHN FHIzWNPGHILKJOHI]^JQ~ξ]eV.ILm*QHRTI]^Jly]j\=bk=D&dHOH_:VqWNj\*QHkHQHOY)]j\=bk=D&doOHIduW&Nj\*QHkHQHOHN Wz]PGHNm*OHNPRFHIG.Km*Yξ1D , ξ~ 2 , . . .ξr]eV.ILm*QHRTI]^Jly]j\=bk=D&dHOH_:VqWNj\*QHkHQHOY)]j\=bk=D&doξ 1 , ξ2 , . . .OHIduW&Nj\*QHkHQHOHN FHIzG=D&]PFHGHNjm*Nj\*NPOHQHfS~]j\D&v.DK¨]eV.Itm*QHRTξI]^Jl]j\=bk=D&dHOH_:VWNj\*QHkHQHOYξ 1 , ξ2 , . . .]j\=bk=D&dHOHIdWNj\*QHkHQHOHN ~]j\D&v.DK]eVItm*QHRTI]^Jl ξ ZbOHYHHQHdG=D&]PFHGHNjm*Nj\*NPO=QKYuZbOHYHHQHQG=D&]PFHGHNjm*Nj\*NPOHQK F1 , F 2 , .
. .FñBæ¥Ê§ÊhèÑÏã¸ÊÌ ßã ߥÈäã áã§õ ãÛçèããÛä߸ö¼÷ çß»Ê`÷ èò»óËôõ ø ùûúýüËþ¿ÿ/ $0"ÓÒÔ'! 13¤E24ÁÄ5¦Ã6 a/ CE5 7§98: -Ω*;+'< *'= 6><!"6#?"!'<$&%(%(''%*%)+*)+@='A',B-'!*.. 9!8:" "/ $0="DIKC&><*)-=E;++!8F><)!$0L1G*'!A!!' B:-MHEA6D?" '!*?"1GIE!6N0D ;+ H!IE"OJ=AP#QB 7'< 9!8:" .+ER¾xSa xCE T ]j\*Q¸FHNPGHNjmêIFHGHNjm*Nj\*NPOHQHNPRÀ]^JIQJ`stO=D&Y§^ÓÒÔ ºn¦JI`|^JII&stO=DLk=D&N^JnLkJI%IFHGHNjm*Nj\*NPOHQHNaKHW\=KHN^J]rKEb]^J&D&GHNPW&pQHR-&ç:IWGHNPRTNPOHO=DKEZEIGHRaD-I&FHGHNjom*Nj\*NPOHQKv&btm*N^J5mD&O=D5FHI&sPMN&¾x axCE ¤FHGHNjm*Nj\*NPOHQ=N KHW\=KHN^J]rK]PYIGHNPNZEQ\*I&]PIZE]PYHQHR)IFHQo]tD&OHQHNPR»FHGHI]^JG=D&OH]^J.W.D|j\*NPRTNPOJ&D&GHOH_:V¸]PIv_JQHdn]PILm*NPG.M5DiQHRÀD\*UPIGHQJR»FHIo]^JGHINPOHQKmD&OHOHIUPI9Iv&¹NPYJ&DçD&RTI"FHI&OKHJQHNSFHGHI]^JG=D&OH]^J.W.D9|j\*NPRTNPOJ&D&GHOH_V+]PIov_JQHdEKHW\=KHN^J]rKXv.DstIW_-R"mH\=KJNPIGHQHQXWNPGHILKJOHI]^JNtdnLQntYD&Y]j\*Njm*]^J.WQHN&nOHNPZEIGoRaD\*QsPbNPRT_-RÑ J&D&YMN&nYD&YOHNPZEIGHRaD\*QsPbNPRTIgFHIOKJQHN)JIkHYHQW§UPNPIRTN^JGHQHQ* jED&YyRT_êbWQm*QHR¸W cnmH\=KuFHI]^JGHINPOHQK+D&Y]PQHIRgJNPIGHQHQWNPGHILKHJOHI&]^JNtdym*I]^J&DoJIkHOHIzIFHGHNjm*Nj\*QJlYD&YLΩ¾x axCE ¿ @ GHQHGHItmD'FHGHI]^JG=D&OH]^J.W.Dy|j\*NPRTNPOJD&GHOH_V QH]eV.Itm*IWHnYD&YFHG=D&WQ\*IHnO=D&]5QHOJNPGHNP]PIW.DJl+OHN5v&bLm*N^JnFHI]PYI\*lYbqRaDJNPRaDJQHkHNP]tYIN9IFHQH]tD&OHQHNOHN[W]PNPUemDXWI&stRTILM9OHIH.NPROHN[RTNPOHNPN&nWsLDmDk=DVn.]PW&KsLD&OHOH_:V9]%|j\*NPRTNPOJ&D&GHOHIdΩJNPIGHQHNPdWNPGHILKJOHI]^JNPdn*FHI]^JGHINPOHQHNv_-W.DN^JzFHI\*N^stOH_-R-nDQHOHIUemDQyOHNPIvLV.IoΩm*QHRT_-R-nsLD&OKJQHNPR-nvN^sYI&JIGHIUPIFHG=D&WQ\*lOHINcGHN^pNPOHQHNcsLDmDkHQ"W&IIv&iNcOHNPWI&s^oRTILM9OHIH¤EÁ Ä ¦Ã aCE ¯ SS [GT QA*'U;IEVA!HW 798:-&YX !"#!&$Z !'%*+)D3 '[' !"#!&$3 *.[/ $0"'\ ]!;+$+^VD\ !_A*<!+ !"#!$&%'`%*)+RUa*.!b cWde(fhgi4jUA^!B'<C5 ><!3D;+\= *!!><"'#^M-*- / $0"'V+AHE6*'U?";'<*k m)-Cl!-B 7'(H-\ 7 !"'#+ 7 7$0HG1[- / =$0.."'!6nD;+HIE"D VR¾xSa xCE £H:N^s^m*NmD\*NPN&n&NP]j\*QOHN:IUPIWIGHNPOHIFHGHI&JQHWOHIN&n&RT_v&bLm*NPRIvI&stO=DLk=DJl)|j\*N^RaN^OJ&D&GHOH_%N'QH]eV.ILm*_ÀkHNPGHN^s nDFHGHI]^JG=D&OH]^JWIq|j\*NPRTNPOJD&GHOH_VωQH]rV.Itm*IW{}kHNPGHN^s Ω¾x%ÄSxTxì [ÁD&]P]PRaDJGHQHW.D&N^J]K|PY]PFHNPGHQHRTNPOJn[sLD&Y\*fck=D&f[iQHdH]rKW§m*Wb.oYHG=DJOHIR`FHItm*vG=D&]P_-W.D&OHQHQ9RTIOHN^J_¤FHQH]tDJlSFHGHI]^JG=D&OH]^J.WIS|j\*NPRTNPOJ&DGHO=_:V9QH]joVItm*IW nH]PII&JWN^J]^J.W&bf[iNPNS|PY]PFHNPGHQHRTNtOJ&b.ΩÁaCE -:I]PFHI\*l&sPbNPRT]KqIFHGHNjm*Nj\*NPOHQHNPR¥ XmH\=K)FHI]^JGHINPOHQK :Y]joFHNPGHQHRTNPOJS]PI&]^JIQJXQsm*W&b.VFHItm*vG=D&]P_-W.D&OHQHd5RTIOHN^J_nFHI|^JIR¦bQH]eV.ILmWΩ_-F=Dm*N^JUPNPGHvcOHN[v&bLm*N^JIFHQH]P_-W.DJlGHN^sPbt\*lJDJ5|^Y]PFHNPGHQHRTNPOJ&D=¤[m*O=D&YIHn][FHIRTI&ilfêQH]joVItmDqWFHNPGHWIR»FHILm*vG=D&]P_-W.D&OHQHQ¸W_-F=Dm*N^JUPNPGHvHnWI`W&JIGHIR»FHILm*vG=D&]P_-W.D&OHQHQW_-F=Dm*N^JzUPNPGHvcbM5NRTILM9OHIIFHQH]tDJl5Itm*QHO'QsEWI&stRTILM9OH_:V'GHN^sPbt\*lJDJIWz|PY]PFHNjoGHQHRTNPOJ&D.¾D&YILm*QHGbNPRqW_-F=Dm*NPOHQHNUPNPGHv.DQW_-F=Dm*NPOHQHNGHN^pN^J.YHQ5]PII&JWN^J]^J.WNPOoOHIzv&bYHW.D&RTQ"UjQ'GHIUemDFHGHI]^JG=D&OH]^J.WI9|j\*NPRTNPOJD&GHOH_VQH]eV.Itm*IWqpom UPU UPG GHU GHGΩ={ ,,,},IkHNPWQm*OHIHnbLm*IW\*NjJWIGKHN^J+IFHGHNjm*Nj\*NPOHQHfæ nDy]j\*Njm*IW.DJNj\*lOHIHnKHW\=KHN^J]rKI&JoWN^JIRgsLDmDkHQ¾x%ÄSxTxû ÁD&]P]PRaDJGHQHW.D&N^J.]K`]j\*Njm=bf[iQHd|PY]PFHN^GHQHRaNPOJTuIOHN^JD+FHItmHovG=D&]P_-W.D&N^J]rK5m*IJNjV5FHIGnFHIYDWFHNPGHW_-N%OHN-W_-F=Dm*N^JXUPNPGHvH¤FHQH]tDJlXFHGHI&]^JG=D&Oo]^JWIz|j\*NPRTNPOJ&D&GHOH_VuQH]rV.Itm*IW nH]PII&JWN^J]^J.W&bf[iNPNS|PY]PFHNPGHQHRTNtOJ&b.ΩÁaCE -IOKJOHIHnkJI mD&OHOH_-d|PY]PFHNPGHQHRTNPOHJnkHQH]^JI`JNPIGHN^JQHkHNt]PYHQnRTIMN^JFHGHItm*I\=M5DJl]KSvNP]PYIOHNPkHOHI[m*I\*UPIH&Á¦D&]P]PRTI&JGHQHRq]PII&JWN^J]^J.W&bf[iQHN-|j\*NjoRTNPOJ&D&GHOH_-N)QH]eV.ILm*_}]j\=bk=D&N+W_-F=Dm*NPOHQKUPNPGHv.DW`FHNPGHWIR;FHILm*vG=D&]P_-W.D&OHQHQ|PY]PFHNPGHQHRTNPOJ9FHGHNPYHG=DiDN^J.]rK T]j\*QyWFHNPGHWIR§FHItm*vG=D&]P_-W.D&OHQHQyW_-F=D\DGHN^pN^JoYDnJI|PY]PFHNPGHQHRTNtOJzFHGHItm*I\=M5D&N^J]KHI]j\*NW&JIGHIUPIFHItm*vG=D&]P_-W.D&OHQK'|PY]PFHNPGHQoRTNPOJFHGHNPYHG=DiD&N^J.]rK"JI\*lYISWEJIR]\=bk=D&N&nN^]j\*Q"W_-F=DmD&N^JUPNPGHvH¯JD&YzmDL\*NPN&¦D&YHQHR¥IvG=DstIR-nTWI]PFHI\*l&stIW.D&W&pQH]PlIvI&stO=DLkHNPOHQKHRTQgsLDmDLkHQ¯ nTFHI\=bk=D&NPR-nkJI9FHGHI]^JG=DOH]^J.WI9|j\*NPRTNPOJ&D&GHOH_:V]PIv_JQHdQHRTNPN^J9WQm[om !U GHU GHGHUΩ={ ,,, ...,GHGtPeGHU, .
. .}. _G=D&]P]PRTI&JGHNj\*Q+m*W.Dz|PY]PFHNPGHQHRTNPOJDêFHNPGHWIR|PY]PFHNPGHQHRTNPOJ.NFHGHI&]^JG=D&Oou]^JWI|j\*NPRTNPOJ&D&GHOH_VQH]rV.Itm*IWIFHQH]P_-W.D&N^J]rK5YIOHNPkHOH_-RqRTOHILMNP]^JWIR-nWIcW&JIGHIR{}]PkHN^JOH_%R¸RTOHILM5NP]^JWIR-¤EÁ Ä ¦Ã aC û @ M !"#!&$4%'%*+)L!+;$+.^M)'=-"!$& Cl-B'Q*^-U^^Q / -DCl>U\ r>U"!$& VRs jtvuWw Þ.ÙPٮ߫PÙÛHÚ«SÚ Øx «¬« w «H®«ª« x Úy{ztÚ&Ù9zt®ÓÒÔ T¤EÁĦÃaCE¸ £Hq|0 / $0"'\ }''~\HE><1!v$Y _- / $0"'\ _!;+$+.^~6 / A*)- 798:-A+ Ω R¾xSaxCEÔ¢IWIG.KJnkJI"- / $0"' A*'U;*kL nNP]j\*QFHGHIQstI&pX\*I\*fcvIN|j\*NPRTNPOJD&GHOHINz]PIv_JQHNnO=Dst_-W.D&ANPRTIN5W'|^JIR¯]\=bk=D&N / P#*A'!.ω∈A^!+HE6?"'<¯ ]PIv&_JQHf A [¾ x%ÄSxax @ [ÁD&]P]PRaDJGHQHW.D&N^J.]rK|PY]PFHNPGHQHRTNtOJn[sLD&Y\*fck=D&f[iQHdH]K1W§m*W&b.oYHG=DJOHIRFHItm*vG=D&]P_-W.D&OHQHQzRTIOHN^J_¤FHQH]tDJlX]-FHIRTI&ilf|j\*NPRTNPOJD&GHOH_Vz]PIv_:oWI"W&JIGHIRFHItm*vG=D&]P_-W.D&OHQHQJQHdnIFHGHNm*Nj\*NPOHOH_VqW9sLDmDLkHN" n]^Iv_JQKA={W_-F=Dm*N^J9UPNPGHv QGHN^pN^J.YDzOHNEW_-F=Dm*N^J5m*W.DG=DsLD5FHItm*GKm } B={}ÁaCE -¤kHNPWQm*OHIHnakJI]PIv_JQHfv\D&UPIFHGHQKJ]^JW&bfcJ \*Qpl|j\*NjoRTNPOJD&GHOH_-Nc]PIv_JQK5UPUj-QGHUj&nD]PIv_JQHf A {¥W]PN[|j\*NPRTNPOJD&GHOH_%Nc]PIv_JQKnsLDQH]PY\*fckHNPOHQHNPRÀGHG¦D&YHQHR;IvG=DstIR-n B UPU GHU QUPU UPG GHU A = { , } B = { , , }NPGHWIO=DLk=D\*lOHI]PkHQJD\*I]PlHnkJI \*fcv.DK¨]^IWIYbFHOHI]^Jl|j\*NPRTNPOJD&GHOH_V¸]PIv_:oJQHdqRTIMN^J']PII&JWN^J]^J.WIW.DJluOHNPYI&JIGHIR¦b)]j\=bk=D&dHOHIR¦b)]PIv_JQHfSRTNPOHOHIyFHI|^JId¸FHGHQHkHQHOHN+FHGHNjm*FHI\D&UjD\*I]PlHnkJI`]PIv_JQHNPR;KHW\=KHN^J]rKg\*fcvINFHItm*RTOHILM5NjoOHN]^JWI HED&Y'RT_bWQm*QHRgWSmD\*lOHNPdpNPR-n=RTOHILMNP]^JWI5W]PNjV'FHItm*RTOHIMNP]^JWW]PNPUemΩDKHW\=KHN^J]rKybtm*IvOH_-R¨Iv&¹NPYJIR-nHIFHQH]P_-W.D&f[iQHR¨Y\D&]P]EW]PNjVyWI&stRTILM9ΩOH_:V]PIv_JQHd&½cMNW ¢[O=D&Rqv&bLm*N^JbLm*IvOHIG=D&]P]PRaDJGHQHW.DJlXRTOHILMNP]^JWIHn]PI]jJIKiNPNQs:kHN^J_-GHNjVWI&stRTIM9OH_VX]PIv_JQHdnFHGHQJIR-nkJIRTOHILMNP]^JWIcW]PNjVXFHILm*RTOHILMNP]^JWRTILMN^JzQHRTN^Jl9]PYI\*l5bUPItm*OHIzvI\*l&pSbfÇRTI&iOHI]^JlH¤EÁ Ä ¦Ã aCE ;Ô¢om T//-- /$0"^!'!?6 -( 'UR;( / -;+ !>U!"!#'@9! |h$&H+% @- */ 1nR$0"- '!1U$0C"A'!1'!!A)' #B8F!?";+'<$%+- /$0"^'!-6 A$0"''D' CBA∪B¤EÁĦÃaCE¿ *'U;)+!'\ - / $0"'!1/8F$0"?"''<D%QC-- / $0"^!'!?6 -'U'Q;-D / \$0 "'!!6"#!R$& %J/ --;+ !/ $0>U"!'!'1U9C *)AC 'DB\ !!R ;+$+A'!!^)-9..ABAB A ∩ B¤EÁĦÃaCE;Ôh0;+"IO- / $0"'!1'"/ #!$&%,- / $0/ "'!1UCqA'!!)#8F?"'<%~- / $0"'!6 AACqWB-A'!!*'!)#8F'U;,D?"'<\ %~-!*..$0"'!6 B Rl -;+!>U!'9 A\B R¤EÁĦÃaCE` Ö !|0 / $0"' !;+$+^)B!$& F- / $0"' VR|0 / $0"' ∅ = Ω\Ω v;+$5+#`^M-Ω-;9 98F!$& 3- / $0"' VR¾xSa xCEÅ :ÄE\=K\*fcvIUPIgFHGHI]^JG=D&OH]^J.W.Dg|j\*NPRTNPOJ&D&GHOH_:V1QH]eV.Itm*IWW]PNPUemDgIFHGHNjm*Nj\*NPOH_Åm*I]^JIWNPGHOHINQêOHNPWI&stRTIM9OHINq]PIv_JQHN&n[FHI]PYI\*lYbmH\=K\*fcvIUPI5RTOHIMNP]^JW.D]^FHG=D&WNjmH\*QHW_1WY\*fckHNPOHQKQΩΩ⊂Ω ∅⊂Ω¤EÁ Ä ¦Ã aCE ` /- / $0"'\ Z=~ - / $0"'! 6 A R |0 $0"' A = Ω\A !;+$+^)+*A!'!BIE!$& ¤EÁĦÃaCE |0 / $0"'<^'!+;$+6Q^9 "!&$7 U'CA B-B' AB = ∅ RSb!cWde(fhgi4j@¾ x axCE ¨Ô.CNP]j\*ILM9OHIsLD&RTN^JQJ.lnkJIXRTN^M5m=bIFHNPG=D&HQKHRTQzO=Dm"]PIov_JQKHRTQQIFHNPG=D&HQKHRTQO=DmRaOHILMNP]^JW.D&RTQ]^biNP]^J.W&b.N^JgFHGKHRaDKD&O=D\*IUPQK¦D&YnO=D&FHGHQHRTNPGn]^bRTRaDEm*W&b.V"]^Iv_JQHdQWSJNPIGHQHQ'RTOHILMNP]^JWO=Dst_-W.D&N^J]KA BIv&¹Njm*QHOHNPOHQHNPRQIvI&stO=DLkHNPOHQK¸FHGHQ¸|^JIRÀ]^IWF=DmD&f[J j-¤[m*O=D&YIHnQH]^JIoA BGHQHkHNP]PYHQ]j\*IM9Q\*I]PlJD&Yn=kJI5JNPIGHQKWNPGHILKJOHI]^JNPd+QH]PFHI\*l&sPbN^J"]PWIf1JNPGHRTQoOHI\*IUPQHf¿FHGHQuG=D&vI&JNX]ERTOHIMNP]^JW.D&RTQo]PIv_JQKHRTQn*FHI|^JIR¦byUPG=D&RTI&JOHNPNSO=Dst_:oW.DJl5FHNPGHNPkHQH]\NPOHOH_%NEIFHNPG=D&HQHQyQHRTNPOHOHIJD&YnHYD&Y'IOHQ'v_:\*QyIFHGHNjm*Nj\*NPOH_*NPROHNSRTNPOHNPN&nOHNS]^JIQJ'sLD&v_-W.DJlHnkJI"FHI9]PWINPd+]^bJQq]PIv_JQHNNP]^Jl'OHNSkJI"QHOHIN&nYD&YyRTOHILM5NP]^JWIHnHFHI|^JIR¦byFHGHQuG=D&vI&JN]E]PIv_JQKHRTQv_-W.D&N^JzFHI\*N^stOHI9D&YJQHWOHIFHI\*l&stIW.DJl]rKzFHGHQHNPRaD&RTQJNPIGHQHQ9RTOHILMNP]^JWHn.DJD&YM5N-GHQH]PIW.DJlEQ\H\*fc]^JG=D&HQHQnFHIRTIU^D&f%iQHNEIHNPOHQJlHnHkHNPR§v&bLm*N^JKHW\=KJl]K"JIQ\*QyQHOHIN]PIv_JQHN&*CEDGHQH]^bOoYDV" ^o @ QstIvG=DMNPOH_1 sLDpSJGHQVIW.D&OH_[ ¦]PII&JWN^J]^J.WNPOHOHIX]^bRTRaDnFHGHIQstWNjm*NjoQ OHQHNXQyG=DstOHI]^Jl9]PIv_JQHdAΩBΩABΩABABÏd»¼±º}£¾ £ÏdÇ»´±´º £¾ ¤Ïd»¼±º £¾ ÓÒÔ %¤EÁĦÃaCE &{a`U^!C><;+)!$4B^!""'SD !.><"# !$&%'%*)+*C-B'! Ω ;+)!M-*'v!\IE!*^n0HE!=E!'<^ P "=*^<CXP(ω) = 1.(1.1)',1R D P#`U^vCh><0HE!=E!'<^ P ;+)r! Ω A)+\!'B^!"*.
ÓÒÔ ¤EÁ Ħ Ãa CE [ v@B#^!""IE6:- / $0"'<^ A !;+$+^~><'.ω∈ΩSP(A) =XP(ω).(1.2)ω∈A¾x axCE ¥ Ö ¤FHGHNjm*Nj\*NPOHQHN+ KHW\=KHN^J]rKY\D&]P]PQHkHNP]PYHQHR¯mH\=K |j\*NjoRTNPOJ&D&GHOHIdgJNPIGHQHQ¨WNPGHILKJOHI]^JNPdnaNPUPIRTILM9OHIqO=D&dJQ¨WIqW]PNjV§bkHNPvOHQHYDVgFHI|^JIdum*QH]PHQHF\*QHOHN&GHQ|^JIR¸QHRTNPOHOHI9IOHIzWIzRTOHIUPIR¨Iv&b.]j\D&W\*QHW.D&N^J9OHNPFHIOHQoRaD&OHQHN5JIUPIHnkHNPR1QHRTNPOHOHIyKHW\=KHN^J]KWNPGHILKJOHI]^JlH¦¾D&RTN^JQHR-nkJIuWuIFHGHNjm*Nj\*NjoOHQHQ' WN^GHIKJOHI]^JlIFHGHNjm*Nj\=KHN^J.]rK5YD&YZbOHYHHQK|j\*NPRTNPOJD&GHOHIUtI]PIv_JQKn.DWIFHGHNjm*Nj\*NPOHQHQu {ÇYD&YZbOHYHHQK5]PIv_JQKnJINP]^JlEOHNPYI&JIGHIUPIERTOHILMNP]^JW.D[s jtvuWw Þ.ÙPٮ߫PÙÛHÚ«SÚ Øx «¬« w «H®«ª« x Úy{ztÚ&Ù9zt®t£|j\*NPRTNPOJD&GHO=_:V9]PIv_JQHdJIEMNKHW\=KHN^J]KzIv\D&]^JlfIFHGHNjm*Nj\*NPOHQK"WN^GHIKJOHIo]^JQ*w5¯v_J&bRT_FHGHQHW_-Y\*Q D&]P]PIHQHQHGHIW.DJl'WNPGHILKJOHI]^JlyQHRTNPOHOHI"]PI"]j\=bk=D&doOH_-R ]PIv_JQHNPR-JNPIGHQHQ5WNPGHIKJOHI]^JNPdmD&OHOH_-d5FHItmHVItm9I]^JD&N^J]rKz]PFHG=D&WNjmH\*QoW_-R-nLJINP]^JlWNPGHILKJOHI]^Jl:NP]^JlZbOHYHHQKn&IFHGHNjm*N\*NPOHO=DKO=DcRTOHILMNP]^JWN]j\=bk=D&dHOH_:VnD'OHN5|j\*NPRTNPOJD&GHOH_Vn]PIv_JQHdÄE\=K)JIUPIHnkJIv_¥W"mD\*lOHNPdpNPROHNcFHGHQV.Itm*QJl5Y9F=D&G=Dm*IY]tD\*lOH_R§W_-WItmD&R-nYD&]tD&f[iQHRT]rK'Iv\D&]^JQ"IFHGHNjm*Nj\*NjoOHQK§WNPGHILKJOHI]^JQn¦m*IUPIWIGHQHRT]K§IFHGHNjm*Nj\=KJl|j\*NPRTNPOJD&GHOH_%NuWNPGHILKJOHI]^JQ¨OHNO=D|j\*NPRTNPOJ&DV n*DO=D5Itm*OHI&JIkHNPkHOH_:VFHItm*RTOHILMNP]^JW.DV ç:II&JOHI&pNPOHQKÓ ΩQ`Ó :FHG=DWQ\*ΩlOHNPNEsLD&FHQH]P_-W.DJl9W5WQm*N--PD)[XP({ω}) = 1ω∈ΩQP(A) =]PII&JWN^J]^J.WNPOHOHIHXP({ω})ω∈AS ^!""*1 B*1¾ x axCE ¼ ½cMNus^m*NP]Pl§]j\*Njm=bN^J¨IUPIoWIGHQJl]rKnkJI'WNPGHILKJOHI]^Jl"JD&YMNSO=Dst_-W.D&f[J=sM9QstOHNPOHOHIdzFHG=D&YJQHYHQzQABbGHIYIWZEQstQHYHQO=D&R)QstWNP]jJO=IHn&kJIRTNPG=D&RTQSJD&YM5NKHW\=KHf[J]rKumH\*QHO=DnF\*I&iDm*lHnIv&¹NPR-n=RaD&]P]tD:NPGHIoKJOHI]^JlHnFHIz]^bJQnOHQHkHNPROHNEI&JL\*QHk=D&N^J]rK+I&J9FHNPGHNjoCkHQH]j\*NPOHOH_:V'ZbOHYHHQHd'RTOHIMNP]^JWHnNP]j\*Q'OHN]PkHQJDJl]PWIdH]^JW.Dg b]j\*IWQHNqÓ L r jnYIoJIGHINUr\D&]PQJLn.kJIWNPGHILKJOHI]^Jlm*I]jJIWNPGHOHIUPIE]PIv_JQK5W]PNPUemDG=D&WOKHN^J]rK5Njm*QoOHQHHN&TI|^JIR¦b`FHGHQ§FHItm*]PkHN^JNyWNPGHILKJOHI]^JQg]j\*IM9OHIUPI)]^Iv_JQKnT]PI]^JILKiNPUPIQs]^bRTR-nFHGHIQstWNjm*NPOHQHd'Q"G=DstOHI]^JNPdyvI\*NPNcFHGHI]^J_:V']PIv_JQHdnv_-W.D&N^JFHI\*N^s^oOHI+I&JOHI]PQJl]K§YWNPGHILKJOHI]^JQ§YD&YnO=DFHGHQHRaN^Gn¦YF\*I&iDm*Q¦CED+GHQH]^bOHYN) £sLDpSJGHQV.IW.D&OHI¸]PIv_JQHNn-YI&JIGHIN ZEIGHRaD\*lOHIgQHRTNPN^Jgm*IWI\*lOHIg]j\*ILM9OHINDW_-G=DMNPOHQHNΩÏdÇ»´±´º £¾ Q.`E 7'+!"'D = (A ∪ B ∪ C)\(A\(B ∪ C))\(B\(A ∪ C))\(C\(A ∪ B))\ABC,HO IzQsSGHQH]^bOHYDzWQm*OHIHn*kJI5mH\=KuW_-kHQH]j\*NPOHQKm*I]^J&DJIkHOHIzstO=DJl9WNPGHILKHJoP(D)OHI]^JQ]PIv&_JQHdnnQnHFHGHQHkHNPRABC AB ACBCP(D) = P(AB) + P(AC) + P(BC) − 3P(ABC).(1.3)ÄD&OHOH_-dXFHItmHV.ILmOHN¦mD&N^J[]^JGHIUPIUPIcRaDJNPRaDJQHkHNP]PYIUPIcGHN^pNPOHQKXsLDmDLkHQnLILm*O=D&YIHnIOEFHI\*N^stNPOEJNPR-nLkJI[FHI&stWI\=KHN^J[FHIOKJlHntkJI%JGHNPv&bN^J.]KSO=DdJQxYD&YEQstWNP]^JOHIHnFHIOKJl5sLDmDLkb9{ästO=DkHQJ9O=DFHI\*IWQHOb'GHN^pQJl9NPN&ça\*Njm=bf[iQHNyJGHQg]PWIdH]^JW.D+KHW\=KHf[J]K§I]POHIWOH_-RTQg]PWIdH]^JW.D&RTQgWN^GHIKJOHIo]^JQb!cWde(fhgi4j [ @ nP(∅) = 0 P(Ω) = 1~P(A ∪ B) = P(A) + P(B) − P(AB)P(A) = 1 − P(A)¢~¾ x%ÄSxTxÀ £H=CED&dJQWNPGHILKJOHI]^Jl9FHIKHW\*NPOHQK'V.I&JLKv_¯Itm*OHIUPIzUPNPGHv.D5FHGHQm*W&bYHG=DJOHIR¸FHItm*vG=D&]P_-W.D&OHQHQRTIOHN^J_1W5G=D&RTYDV'b]j\*IWQKysLDmDkHQ ÁaCE -*b.]^Jl{ä]PIv_JQHN&n*WNPGHILKJOHI]^Jl9YI&JIGHIUPIJGHNPv&b.N^J]KO=D&doAJQLÄE\=KXJIUPIHnkJIv_W_-kHQH]j\*QJlOHNPIvtVItm*QHRTI[sLDmDJlWNPGHILKJOHI]^JQO=D%ILmHoP(A)OHI&JIkHNPkHOH_:V FHItm*RTOHILMNP]^JW.DVǤFHGHNjm*Nj\*QHR QV ]j\*Njm=bf[iQ=R IvG=DstIR-hUPUnUPGn Ω GHUnGHG¦D&YIFHGHNjoP({ }) = 0.1 P({ }) = 0.2 P({ }) = 0.3 P({ }) = 0.4m*Nj\*NPOHO=DK¸ZbOHYHHQKbLm*IW\*N^JWIG.KHN^JIFHGHNjm*Nj\*NPOHQHf n¦JI`NP]^JlKHW\=KHN^J]rKWNPGHIKJOHI]jJlfS¾D&RTN^PJQHR-nkJIUPU UPG GHU Eça\*Njm*IW.DJNj\*lOHIHnA = { , , }P(A) =0.1 + 0.2 + 0.3 = 0.6-¤EÁ¤Eçcu_¯stO=D&NPR-n*kJI9WNPGHIKJOHI]^Jl"FHILKHW\*NPOHQKuUPNPGHv.DzFHGHQItm*OHIYHG=DJoOHIRÀFHILm*vG=D&]P_-W.D&OHQHQRTIOHN^J_ûG=D&WOKHN^J]KWNPGHILKJOHI]^JQêFHILKHW\*NPOHQKGHN^pN^JYHQIkHNPR¦b'W]PNEWNPGHIKJOHI]^JQW5GHN^pNPOHQHQsLDmDLkHQ £5G=Ds^\*QHkHOH_[w¤[ T:-CED§]tD&RTIRÀm*Nj\*N&n[WIFHGHI]q]j\*Njm=b.N^JFHI]^JD&WQJl¨pQHGHN&h%YD&YHQHR}IvoG=DstIR¯RTILM9OHIyI&FHGHNjm*Nj\*QJ.lWNPGHILKJOHI]^JQ]PIv_JQHd*w5ÄSIyO=Dk=DL\D ÀWNPYD'FHGHNjoIv\DmD\qY\D&]P]PQHkHNP]PYHQ=dqFHItmHVItm Y+IFHGHNjm*Nj\*NPOHQHfÀW&NPGHIKJOHI]^JNPdq]PIv_JQHdçD&R|^JI&J¨FHItmHVItm1v_:\¯I]POHIW.D&OO=Dm*W&b.VFHGHQHOHHQHF=DVh[D&FHGHQHIGHOHIR}Q]^JDJQH]^J.QHk=Njo]PYIR-¦:IoFHNPGHW_:Vn¦RT_ÀRTILM5NPRFHI\*ILM9QJl)WNPGHILKJOHI]^JQgOHNP]PYI\*lYHQV§]PIv_JQHdG=D&WOH_-RTQuRTN^M5m=b']PIvIdnHNP]j\*QOHNE]^biNP]^J.W&bNPJ"FHIWItmD]PkHQJDJl9YD&YINjoºJIz]PIv_oJQHNSvI\*NPNFHGHNjm*FHIkJQJNj\*lOH_%RnOHN^MNj\*Qym*GbUPQHN& JI"D&FHGHQHIGHOH_:VFHItmHV.Itm]^J&DJQH]^J.QHkHNP]tYIR+FHItmHVItm*NaFHGHIWItm*QJ]Km*I]^JDJIkHOHIcvI\*l&pINTYI\*QHkHNP]^JWIc|PY]PFHNjoGHQHRTNPOJIWHn&QWNPGHILKJOHI]^JlE]^Iv_JQKFHI\D&U^D&f%JG=D&WOHIdFHGHNjm*Nj\=bSI&JOHI]PQJNj\lOHIdk=D&]^JI&J_FHILKHW\*NPOHQKu]PIv_JQKÇ]j\=bk=D&Nz]5FHG=D&WQ\*lOHId Qm*NtD\*lOHIdRTIOHN^JIdRT_¥OHNzRTILM5N^R1D&FHGHQHIGHQ I&JomDJlFHGHNjm*FHIkJNPOHQ=N-OHQItm*OHIdQs-]^JIGHIORTIOHN^J_nFHI|^JIR¦bE\*IUPQHkHOHIFHI\*ILM9QJlWNPGHIKJOHI]jJl¯W_-F=Dm*NPOHQK¿UPNPGHv.DG=D&WOHIdÇWNPGHILKJOHI]^JQ»W_-F=Dm*NPOHQK¿GHN^pN^JYHQÄE\=K'JIUPIn=kJIv_êFHGHIWNPGHQJlzFHG=D&WQ\*lOHI]^JlJD&YHQVyG=D&]P]^bM5m*NPOHQHdu]^JDJQH]^J.QHk=Njo]PYHQzRTILM9OHIFHGHIWNP]^JQ9]PNPGHQHfIFH_JIWXQ5W_KH]POHQJlHn.YD&Y5WNjm*N^JX]PNPvLKzI&JOHI]PQJNj\*loO=DKzk=D&]^JI&JDSFHILKHW\*NPOHQKn.]PYDMNPR-n.UPNPGHv.D.¦D&YzWIEW&JIGHId9FHI\*IW&QHOHN¦WNPYDËÃz¦ :fcZEZEIO§FHGHIWNj\¨£ £ FHItm*vG=D&]P_-W.D&OHQHdgRTIOHN^J_nTFHGHQg|^JIR¿UPNPGHv W_:oF=D\ & £ Ö G=DsIJOHI]PQJN^\*lO=DK"k=D&]jJI&J&DXG=D&WOKHN^J]K Ô¢ Ö j~FHI&sPM5N&nbMN%WXYIOHHNÀWNPYDnQHGH]PIOqFHGHIWN\ £ FHILm*vG=D&]^_-W.D&OHQHdnUPNPGHv'W_-F=D\¨ & G=DsI&JOHI]PQJNj\lO=DKyk=D&]^JI&JDG=D&WOKHN^J]rK Ô¢ ¢ j.ÄSNPdH]^JWQJNj\*lOHIHn=YD&Y'RT_WQm*QHR-nFHGHQ§bWNj\*QHkHNPOHQHQ¨kHQH]j\D)QH]jok=D&]^JI&J&DqFHILKHW\*NPOHQK§UPNPGHv.DqFHGHQHv\*QM5D&N^J]rKgY1/2FH_J&D&OHQHdRTNPOHOHIy|^JIyIv]^JILKJNj\*l]^J.WIuFHI]j\=bM9Q\*IyFHIW&ILm*IRY)IFHGHNjm*Nj\*NPOHQHfom G{p[W[W` [ [s jtvuWw Þ.ÙPٮ߫PÙÛHÚ«SÚ Øx «¬« w «H®«ª« x Úy{ztÚ&Ù9zt®LW NPGHILKJOHI]^JQ']PIv_JQKYD&Y9FHGHNjm*Nj\DSI&JOHI&pNPOHQK"kHQH]j\DFHILKHW\*NPOHQHd9]PIv_:oAnAJQKW |PY]PFHNPGHQHRTNPOJ&DVQukHQH]j\D5|PY]PFHNPGHQHRTNPOHJIWHhAnP(A) = n→∞limnA.n(1.4)Á uQstNP]PIRv_:\DFHGHNjm*FHGHQHOKJDm*IWI\*lOHIb]PFHN^pO=DKzFHIFH_JYDEFHI]^JGHINPOHQK]PQH]^JNPRT_¸D&Y]PQHIR-n&I]POHIW.D&OHOH_:VO=Dc]PII&JOHI&pNPOHQHQ+Ó £ jçD&RT_-R ]j\D&v&_-R RTNP]^JIRpYI\*_¼uQstNP]tD)KHW\=KHN^J]KgOHNPWI&stRTILM9OHI]^Jl FHGHIWNjm*NPOHQKgvNP]PYIOHNPkHOHIvI\*l&pIoUPI)kHQH]j\D)|PY]PFHNPGHQHRTNPOJ.IW)mH\=KW_KHW\*NPOHQK§W]PNjVk\*NPOHIW)FHI]j\*Njm*IW.DJNj\*lOHI]^J.QmH\=K O=DV.ILM5m*NPOHQK FHGHNjm*Nj\D`Ó £ jçÇFHILKHW\*NPOHQHNPR1]PQH]^JNPRT_ÀD&Y]PQHIR{nA /n}n≥1xSHC=I\*RTIUPIGHIW.DRTQstNP]PIW]PYDKyk=D&]^JI&JO=DKypYI\DFHI]^JNPFHNPOHOHIzIYIOHk=DJN\*loOHI%FHI&JNPG.K\D[WNP]TW%O=DLbYN&¤[m*O=D&YIHnt]PFHG=D&WNjmH\*QHWI]^JQSG=Dm*QnL]^JIQJ[sLD&RTN^JQJlHnkJIRTOHIUPQHNQstWNP]^JOH_-N5RaDJNPRaDJQHYHQnFHQH]tD&W&pQHN]PWIQ+]tD&RT_-NQstW&NP]^JO=_-NG=D&vI&J_ÇWG=D&RTYDV5YI\*RTIUPIGHIW]PYIdzD&Y]PQHIRaDJQHYHQn.v_:\*QnJNPROHN-RTNPOHNPN&nFHGHQHWNPG.MNPOH=D&RTQRTQstNP]PIW]PYIUPI9FHItmHV.ILmDçJIQJJ&D&YMN5sLD&RTN^JQJlHnkJIym*I]PQV FHIGFHGHQHOKJI]PkHQJDJlHnkJIFHIOKJQHN]j\=bk=D&dHOHI]^JQ¨Q\*Q+]^JItVD&]^J.QHkHOHI]^J.Q* cRTILM9OHI9FHGHQHRTNPOKJl"JI\*lYI"YJNPR|PY]PFHNjoGHQHRTNPOJD&R-nYI&JIGH_-N"O=D&G.Km=b ]PI]PWIdH]^JW.D&RTQ`OHNjm*N^JNPG=RTQHOHQHGHIW.D&OHOHI]^J.QQ`WI&s^oRTILM9OHI]^JQêFHIW&JIGHNPOHQK¯FHGHQ¯OHNPQstRTNPOHOH_:Vêb.]\*IWQKVêIv\DmD&f[JgJD&YMNq]PWIdo]^JWIRb]^JIdHkHQHWI]^JQ'I&JOHI]PQJNj\*lOH_:V"k=D&]^JI&JJIXMN%YD&]tD&N^J]rK9sLDmDLkHQ £Hn&JIWyOHNPd RT_¥OHNsLDmD&W.D\*QH]PluHNj\*lf;FHI]^JGHIQJlRTILm*Nj\*lHnI&JG=DMzD&f%iSbf;m*NPdH]^JWQoJNj\*lOH_-dê|PY]PFHNPGHQHRTNPOJ%CED&]+QHOJNPGHNP]PIW.D\*I`\*Qpl§ZEIGHRaD\*lOHIN+IFHGHNjm*Nj\*NPOHQHNWNPGHILKJOHI]^JQJD&Yn-JNPFHNPGHl¸v&btm*N^J¸FHIOKJOHIHn-YD&YHQHRTQêFHGHNjm*FHI]P_:\*YD&RTQ1GbYIWItm*]^JWIW.Do\*QH]PlzRaDJNPRaDJQHYHQnHmD&W.DKy]j\*Njm=bf[iNtNSY\D&]P]PQHkHNP]PYINSIFHGHNjm*Nj\*NPOHQHN&¤EÁ Ä ¦Ã aCE @ 'U; n D\ !C ω , .
![](https://s.studizba.com/z.php?f=/templates/si/i/noavatar.png&w=100&h=100&t=1"){kind=avatar}
