А.А. Кудрявцев - Пособие по теории вероятностей (1115312), страница 4
Текст из файла (страница 4)
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w¤kHNPWQm*OHIHn-kJIgWNPGHILKJOHI]^Jlg]PIv_JQKI]^JD&N^J]rKOHNPQstRTNPOHOHIdn¦OHN^sLD&WQH]PQHBRTI)I&J+JIUPIHnFHGHIQstI&pX\*I)]PIv_JQHNQ\*Q`OHAN^J¦INP]^Jl]PFHG=D&WNjmH\*QHWIG=D&WNPOH]^JWI&s-IFHGHNjm*Nj\*NPOHQK B@ :W]^WIf¸IkHNPGHNjm*l]j\*Njm=b.N^JqFHGHQyb]j\*IWQHQ P(A| B) j=n=kP(A)JIP(B) > 0P(AB) = P(A)P(B)¤EÁ Ä ¦Ã aC @ ' [ |0 / $0"'<^ A ' B !;+$+6^~D;++''< 7$& 7'UCY-.P(AB) = P(A)P(B).(3.1)C NT]j\*Njm=bN^JFbJDJlcFHIOKJQKOHNP]PIWRTNP]^JOHI]^J.QcIFHGHNjm*Nj\*NPOHQHN[ QOHN^sLDoWQH]PQHRTI]^JQX]PIv_JQHd¾x%ÄSxTx @ %b.]^JlQ[uIU^bJg\*Q¯OHN^sLDWQH]PQHRT_-N0]PIv_JQKQv_Jl'OHNP]PIP(A)WRTNP]^J>OH_-0RTQw9P(B)uIU^bJ">\*Q+OHNP]PIWRTNP]^JOH_%N]PIv_JQKA BAQv_JlzOHN^sLD&WQH]PQHRT_-RTQ*wBÁaCE -b]^JlQOHNPYI&JIGH_-N5OHN^sLD&WQH]PQHRT_-N5]PIv_JQKqOHNPObL\*NPWIdA BWNPGHIKJOHI]jJQs @ ]j\*Njm=bN^JnkJIt¦D&YHQHRyIvG=DstIR-ntOHN^sLD&WQH]PQHRT_-N]PIv_JQK+FHI\*ILM9QJNj\*lOHId+WNPGHILKJOHIP(AB)]^JQ)OHNX>RTI0U^bJ"v_Jl"OHNP]PIWRTNP]jJO=_-RTQÁD&]jo]PRTI&JGHQHRm*W.D+OHNP]PIWRTNP]^JOH_:Vg]PIv_JQKQFHI\*IM9QJNj\*l&OHId§WNPGHILKJOHI]^JQA B¤kHNPWQm*OHIHnkJI+G=D&WNPOH]^JWIg @ W|^JIRÇ]j\=bk=D&N"OHN9W_-FHI\*OKHN^J]K¦D&YHQHR1IvoG=DstIR-nOHNP]PIWRTNP]^JOH_-N]PIv_JQK+FHI\*IM9QJNj\*lOHId+WNPGHILKJOHI]^JQ)OHNSRTIU^bJ'v_JlOHN^sLD&WQH]PQHRT_-RTQCN^sLD&W&QH]PQHRT_-NS]PIv_JQKuIv\DmD&f[Jz]j\*Njm=bf[iQ=RTQ]PWIdH]^JW.D&RTQhom "NP]j\*QnJI)OHN^sLD&WQH]PQHRTI]^Jlq]PIv_JQHdQ|PYHWQHW.DL\*NPOJO=D)G=Do> 0A BWNPOH]^JP(B)W&b~[ "NP]j\*Q]PIv_JQKP(A| B) = P(A)AQBOHN^sLD&WQH]PQHRT_n=JIAQBJD&YM5NEOHN^sLD&W&QH]PQHRT_~QOHN^sLD&WQH]PQHRT_ÅQê]PIv_JQKQOHN^sLD&WQH]PQHRT_n@ "NP]j\*Q¯]^Iv_JQKA B1A B2FHGHQHkHNPRn JIz]PIv_JQKQOHN^sLD&WQH]PQHRT_B1 B2 = ∅AB 1 ∪ B2s ®<th± Ù w Úªv²[«ª« x Úy¥ztÚÙ9zt®+®u«jÝtÞª®Ùr®v¤Ú&Ù9z*³yÙPÚܲWzt®Hà¾x%ÄSxax @ [ .Á¦D&]P]PRaDJGHQHW.D&N^J]K5m*W&bYHG=DJOHIN[FHItm*vG=D&]P_-W.D&OHQHN[FHG=D&WQ\*lOHIdQm*NtD\*lOHIdRTIOHN^J_-IYDsLDJlHn:kJI]PIv_JQKW`FHNPGHWIRÀFHItm*vG=D&]P_-W.Do[&ÖHO QHQ`W_-F=Dm*N^JqU^NPGHv QWIW&JIGHIRFHILm*v&G=AD&]P_-=W.D&{OHQHQW_-F=Dm*N^J)GHN^pN^J.YD} B = {}KHW\=KHf[J]rKuOHN^sLD&WQH]PQHRT_-RTQÁaCE -¤v_-kHOHIHnOHN^sLD&WQH]PQHRTI]^Jl]PIv_JQHdqm*IYDst_-W.D&N^J]rKOHNPFHI]PGHNjmHo]^JWNPOHOHIdFHGHIWNPGHYIduG=D&WNPOH]^JW.D+ @ j=¨mD&OHOHIR¨]j\=bk=D&NXQHRTNPNPRom UPGP(AB) = P({ }) =¾x%ÄSxax @ @ =b.]^Jl1 11= · = P(A)P(B).42 2Ω = {(ω1 , ω2 )| ω1 , ω2 ∈ [0, 1]}.b]^JlA = {(ω1 , ω2 )| 0 ≤ ω1 ≤ 1, 0 < a ≤ ω2 ≤ 1},B = {(ω1 , ω2 )| 0 < b ≤ ω1 ≤ 1, 0 ≤ ω2 ≤ 1},C = {(ω1 , ω2 )| ω2 ≤ (ω1 − b)/(1 − b), ω1 , ω2 ∈ [0, 1]}BT [ ]PR-GHQH]& @ j.ÁD&]P]PRaDJGHQHW.D&N^J]K9UPNPIRTN^JGHQHkHNP]tYDK9WNPGHILKJOHI]^JlX]PIv_JQHd) j btm=bJ\*Q']PIv_JQKQOHN^sLD&WQH]PQHRT_-RTQ*wX bLm=bJ\*Q"]PIv_JQKQOHNjsLD&WQoA BA C]PQHRT_-RTQ*wÁaC -zGHIWNPGHQHR G=D&WNPOH]^JWI @ Wω2IvIQV]j\=bk=DKV.RTNPNPR1nLJINP]^Jl Q P(AB){OHN^sL=D&W(1−a)(1−b)QH]PQHRT_ÄD\*NP=Nnom P(A)P(B)A BP(AC) = (1 − b)(1 − a)2 /2 6= (1 − a) · (1 − b)/2 =¦D&YHQHR¯IvG=DstIR-n]9FHIRTI&ilf}G=D&WN^OoP(A)P(C)a]^JW.Dê @ 5RT_¼FHIYDsLD\*QI&J]^bJ]^J.WQHNqOHN^sLD&WQH]PQoRTI]^JQQ A CdÏ »¼±ºW¾ £ 7'Q¤(E-Á*Ä=EHE¦A!ÃaCE"'UC5 -@\ @ 'M@)|0U ^~/ $06"/ '<$&^ % B1 ,≤.
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