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- Politecnico di Milano
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- Mathematical Engineering
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- Modelli e Metodi dell'Inferenza Statistica
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G2;;B /B .2 JQ`; M, aB AαĂΩ7 KB;HB /B bQiiQBMbB2KB /BΩ (YαAα)C=XαAC α-(XαAα)C=YαAC α 6 mMxBQM2 KBbm` #BH2, . iB(Ω,A)2(F,F)- mM 7mMxBQM2X:ΩÑFĕ /2ii KBbm` #BH2fp `B #BH2 H2 iQ`B b2, (XPB)PA@BPF _2H xBQMB +QMi`QBKK ;BMB@mMBQMB- BMi2`b2@ xBQMB Q +QKTH2K2Mi xBQMB, X´1(BC)=(X´1(B))C X´1(YαBα)=YαX´1(Bα) X´1(XαBα)=XαX´1(Bα) S`Q# #BHBi¨ /B mM BMi2`p HHQ, P((x, y]) =F(y)´F(x) P([x, y]) =F(y)´F(x´) P((x, y)) =F(y´)´F(x) P([x, y)) =F(y´)´F(x´) P(txu)=F(x)´F(x´) Zm MiBH2 /B Q`/BM2α,# P(Xďqα)ěα P(Xěqα)ď1´α ñ # P(Xďqα)ěα P(Xăqα)ďα ñ # FX(qα)ěα FX(qsα)ďα .2}MBxBQM2 HBKbmT- HBKBM7 2/ 2b2KTBQ, liminf Xn=HBKnÑ+8(infmąnXm) limsupXn=HBKnÑ+8(supmąnXm) A=ǴAM}MBiB eǴEk=Ǵe H H M+BQ FǴ A=limsupEn limsup=X8 n=1YkěnEk P(YkěnEk)=1´P(XkěnEC k) =1´P(HBKmÑ8 Xm k=nEC k) =1´HBKmÑ8 P(Xm k=nEC k) =1´HBKmÑ8 śm k=nP(EC k) =1´HBKmÑ8 śm k=n 5 6 =1´HBKmÑ8 (5 6)m´(n´1)=1 P(A)=P(HBK bmTEk)=P(X8 n=1YkěnEk)=1 T2`+?û 2p2MiB /B T`Q# #BHBi¨ R UYkěnEk? T`Q@ # #BHBi¨ RV B=Ǵa2KT`2 eǴB=XkPNEk P(B)=P(X8 k=1Ek)=HBKnÑ8 P(Xn k=1Ek) =HBKnÑ8 śn k=1P(Ek)=HBKnÑ8 (1 6)n=0 aT xB G, aB `B+Q`/ +?2L12L2bQMQ bT xB p2iiQ`B HBX X:ΩÑRo _PL1ôE[X]PR xPL1ðñ |x|PL1 X, YPLp2X[+=Yðñ[X]=[Y]PLp * m+?v@a+?r `x, X, YPL2ñ|E[XY]|ď a E[X2]E[Y2] XPL2ñE[X]2ďE[X2] .Bbm;m ;HB Mx /B J `FQp, Xo _ñP(|X|ěa)ďE[|X|] a @aą0 .Bbm;m ;HB Mx /B Ì2#vȒďp, XPL2o _ñP(|x´µ|ěa)ďVa r(x) a2 G2KK /B 6 iQm, aB MQ H2 o Xn2Yi HB +?2XněY[+-YPL1X HHQ` E [ HBK BM7n Xn ] ďHBK BM7n E[Xn] h bbQ /B 7 HHBK2MiQ, . iQtą0, hX(t)=HBKϵÑ0+ P(tăXăt+ϵ|Xąt) ϵ hX(t)= fx(t) 1´Fx(t) o HQ`2 ii2bQ 2 KQK2MiBo HQ`2 ii2bQ, E[h(X)] = ş Ωh(X(ω))I(dω) = ş Ωh(X(ω))P(dω)= ş Rh(x)PX(/x) = ş Rh(x)fX(x)/x L2H + bQ /Bb+`2iQ,E[h(x)] =ř kh(xk)pk o `B Mx 2 +Qp `B Mx , Va r(X)=σ2 X=E[X2]´E[X]2- Cov(X, Y)=σXY=E[XY]´E[X]E[Y] Va r(X+Y)=Va r(X)+Va r(Y)+2¨Cov(X, Y) aB MQiB +?2 M2H + bQ KmHiB/BK2MbBQM H2 H p `B M@…
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