Vf%4.a.s.rHome PageTitle PageJJIIJIPage 1 of 190Go BackFull ScreenCloseQuit?IEa 2006c2-7V18:4nIEO7KXWVf%4.a.s.rHome PageTitle PageJJIIJIPage 2 of 190Go BackFull ScreenCloseQuit VdkL4nU, vk4nUVVg.Gnedenko and KolmogorovVf%4.a.s.rHome PageTitle PageJJIIJIPage 3 of 190Go BackFull ScreenCloseQuit 4nV|, SNL.=U3df0 3, n, n N3Vm(,F,P) C ?n, n Nm5Vf%4.a.s.rHome PageTitle PageJJIIJIPage 4 of 190Go BackFull ScreenCloseQuit1V VCSn, n NCm5Vf%4.a.s.rHome PageTitle PageJJIIJIPage 5 of 190Go BackFull ScreenCloseQuit1.1.VVV k5V6.1.1 XJ? 0, klimnP(| n | ) = 0,(1.1)CSn, n NVC, Pnp Vf%4.a.s.rHome PageTitle PageJJIIJIPage 6 of 190Go BackFull ScreenCloseQuit 5, IOVP(| n |). kI7V. I(A)LA5, =kI(A) =( 1, A;0, Ac. o, w , ?A B, kI(A) I(B). kP(A) = EI(A)Vf%4.a.s.rHome PageTitle PageJJIIJIPage 7 of 190Go BackFull ScreenCloseQuitnnn6.1.1(Chebyshev) g(x)30,)K, XJC, kEg(| |) 0a 0, kP(| | a) Eg(| |) g(a).(1.2)Vf%4.a.s.rHome PageTitle PageJJIIJIPage 8 of 190Go BackFull ScreenCloseQuit k, dg(x)5(| | a) ? g(| |) g(a)? . dI(| | a) I? g(| |) g(a)? g(| |) g(a)I? g(| |) g(a)? ,I(A)A5; 1du3? g(| |) g(a)? kg(|)g(a) 1. dP(| | a) = EI(| | a) EI? g(| |) g(a)? E?g(| |)g(a)I? g(| |) g(a)? Eg(| |) g(a).Vf%4.a.s.rHome PageTitle PageJJIIJIPage 9 of 190Go BackFull ScreenCloseQuit Chebyshev, 3Vk2?. X:1. XJC Lr(r 0), okP(| | x) E | |r xr, x 0.(1.3) 3Chebyshev-g(x) = xr=Vf%4.a.s.rHome PageTitle PageJJIIJIPage 10 of 190Go BackFull ScreenCloseQuit Chebyshev, ?f6.1.2n, n NCS,Sn=nPk=1k. XJ3San, n NSbn, n N, Sn an bnp 0,(1.4)=limnP? |Sn an bn| ? = 0, 0,(1.5)n, n Nlf.an, n N %z, bn, n NKz.Vf%4.a.s.rHome PageTitle PageJJIIJIPage 11 of 190Go BackFull ScreenCloseQuit ufCSn, n N 3%zan, n NKzbn, n N, (1.4). XJn L1, n N, oOan=ESn, bn= n, n N, ?Sn ESn np 0(1.6) 5w uffVf%4.a.s.rHome PageTitle PageJJIIJIPage 12 of 190Go BackFull ScreenCloseQuit2.(Markovfff ) X J C Sn, n N, klimnDSn n2= 0,(1.7)okX(1.6)fVf%4.a.s.rHome PageTitle PageJJIIJIPage 13 of 190Go BackFull ScreenCloseQuit 3Chebyshev-g(x) = x2, =, ? 0, ?n , kP? |Sn ESn n| ? = P (| Sn ESn| n)E(Sn ESn)2 n22=1 2DSn n2 0, kX(1.6)f 3MarkovfvkSn, n NCmpX?b, /2(Vf%4.a.s.rHome PageTitle PageJJIIJIPage 14 of 190Go BackFull ScreenCloseQuit3.(Chebyshevfff) XJSn, n NC 3C 0, DnC, n N, okX(1.6)f. dun, n NC, DSn=nPk=1Dk nC,= k (1.7) . dMarkovf ChebyshevfVf%4.a.s.rHome PageTitle PageJJIIJIPage 15 of 190Go BackFull ScreenCloseQuit4.(Bernoullifff)XJnLnBernoulli?g, Kkn np p.(1.8) n=nPk=1k:= Sn, kplpBernoulliC, Ek= p, Dk= pq 1. dChebyshevfkX(1.6) f, =k(1.8).Vf%4.a.s.rHome PageTitle PageJJIIJIPage 16 of 190Go BackFull ScreenCloseQuit 5wKzbn6= nf5. k,31kk1xk 1.gcn,nLnx.K?r 1 2, k n En lnrnp 0 .Vf%4.a.s.rHome PageTitle PageJJIIJIPage 17 of 190Go BackFull ScreenCloseQuit Ck: XJg1kx, -k= 1; XJ, -k= 0. ukpBernoulliC, klpk=1 kBernoulli.Vf%4.a.s.rHome PageTitle PageJJIIJIPage 18 of 190Go BackFull ScreenCloseQuit w,kn=nPk=1k, Ek=1 k,Dk=1 k1 k20. l dChebyshev: ? 0, ?n , kP? |n En lnrn| ? = P (| n En| lnrn)Dn 2ln2rnC 21 ln2r1n 0, nEnlnrnp 0.Vf%4.a.s.rHome PageTitle PageJJIIJIPage 19 of 190Go BackFull ScreenCloseQuit6. 3, k n lnnp 1 .Vf%4.a.s.rHome PageTitle PageJJIIJIPage 20 of 190Go BackFull ScreenCloseQuit y(, IylimnP(| n lnn | lnn) = 0, 0. 5limn(En lnn) = limnnPj=11 j lnn!= c 0,cEuler =, ?n, ? 0, klnn + (lnn En) 1 2lnn. l ?n, kP(| n lnn | lnn) P (| n En| lnn + (lnn En) P? | n En|1