概率论习题答案

123AA=Ω=AAUφ=AAIABABABABBAφ=ABABΩΩφ1334331Ω={34}518L2Ω={012}312AAEΩEAPA()101≤≤PA()2P()Ω=13AAAn12,,,,LL)PAPAiiii()(=∞=∞=∑11UPA()AnAAnnA()nAn)(nnAA2PA()fAPAnn()()→∞⎯→⎯⎯PA()AApAPA()PA()1P()φ=02AAAn12,,,LPAPAiinini()(===∑11U)3AAPAPA()()=−14AB⊂PBAPBPA()()()−=−PAPB()()≤5PABPAPBPAB()()()(U)=+−AAAn12,,,LPAAAPAPAPAPAAPAA()()()()()(1231231213UU=)++−−−+PAAPAAA()(23123))PAPAPAAPAAAPAAiiniijijninijknnijkn()()()()()(==−=−+++−∑∑∑11111ULL3ABΩPB()0PABPABPB(|)$()/(=)BA)|(BAPBA)(AP3)(APA)|(BAPBABAPAB(|)2PAB()PB()PAB(|)ABAB)()()(BPAPABP=)()|(APBAP=ABBayesinAAAAn12LUiiAA1=⊂nnAnAAAAAAAULUU21=nAAAAAAL21iAAA)(iAP)|(iAAP=12LPAii()=∑=11AAAn12LAAAn12L1AAAn12LAAAAAn12LnAnAAAn12LAAAAn12LAAAn12L4A2AAAn12LBBayesPAi()PABi(|))|(1AAP)(AP)(1AP)|(1AAPnn123412nn⇒AB1314CABCiAi4,3,2,1=i41)(=iAP21)()()()(2121=+==APAPAAPAPU21)()(==CPBP)()(41)()]()[()(13121BPAPAPAAAAPABP====UIU)()(41)(CPAPACP==)()(41)(CPBPBCP==ABC)()()(41)()]()()[()(1413121CPBPAPAPAAAAAAPABCP≠===UIUIUABC5