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23[01][01][01])(xf)(xf:)(xf)(xf()xhi()()xhxfii∑=()xhi)(xf()xhi()xhidx∫A.xip(),...2,1=ixi.()∑≤=xxiipxFip1=∑iip[01]ξ()()jjxFxF≤−ξ1jjjxjx=η()jxF:γγspeTσσσσ++=.1.ξ2.Tsσσξ/3.()TesTsσσσξσσ//+≤4.()Tesσσσξ/+≥B.η)(xf.()()dxxfxFx∫∞−=()ξη1−=F()xfx≤η{}(){}(){}()()xFdxdxxFpxFpxpxF=⋅+⋅=≤=≤=≤∫∫∞−−00110ξξη.()xF()xf()=−.,00,0,λλλxexfx.()()xxtxedtedttfxFλλλ−−∞−−===∫∫10ξ[01]()ληηξ−−==eF1(ξ)λη−−=1ln1.ξ−1ξ[01]ξληln1−=.γγγ−−−=xxxf101)(1,0≤γxx.2.3.9101)()()(00−∞+−==∫∫γxxdxxfdxxfxFxxx.[01]ξ()101−−==γηξxxFξ−1ξ[01])1(10−−=γξηx.,()xfηδ()yφ.()ygx=()yg()()xhxg=−1()()(xhxh′⋅φηδη′′,21,ggJx)()yg()()()()xhxhxf′⋅=φ.()yφδ()δg=()xf()yφ[01]()()yyF1−=g()yxf,δη,)v(ug,(vugx,1=))),(vugy,2=(yxhu,1=.()yxhv,2=),()),(),,((21yxfJyxhyxhg=⋅.(Jacobi)yvxvyuxuJ∂∂∂∂∂∂∂∂=.),(vugδη′′,()yxf,δη,1212gghhη()()−−=222exp121σµσπxxf.()xf()2,σµNµ2ση{}µη=E{}2ση=V.1,02==σµ(){}2/exp212xxf−=π.(1,0N)ηδηδµσδη+=.()xFuv,yx,sincosuu()()−=−=.2ln2,2ln2vyvxππ:()()()()≡=≡+−=−yxhxyvyxhyxu,/tan21,21exp21122πxy()()()()Jyxhyxhgyxf⋅=,,,,21.:uv,u()1=vg()()+−=2221exp21,yxyxfπ.:(yxf,)()()()yfxfyxf⋅=,.(){}2/exp212xxf−=π(){}2/exp212yyf−=π.Maraglia1[01]uv2()(221212−+−=vuw)1w/ln2wwz3144()[]2/1−=vzyuzx==,.(VonNeumann)()xf{}nξ()xfiξ()xfiξiξ()xf()xf()xf1.η[a,b]()xf[a,b]()xfλ1)(max],[==∈xfLbax()xfλ[01]],[bax∈(a)[01]1ξ[a,b]1)(ξδaba−+=(b)[01]2ξ()δλξf≤2ca(c)δη={}nη(2.3.1)b()xf()δλξf≤2()λξδ/,2x[()xf],dxxx+()()()dxxfdxxfdxxfba=∫(()xf)λξδ/,2()xf(a)bL−()()()abLabLdxxfEba−=−=∫1.L()xfη()≤≤=.,0,10,2xxxf.()2xxF=[01]ξ.2x=ξξ=x.xη()22maxmax]1,0[]1,0[==≡∈∈xxfLxx.1.[01]21,ξξ2.()1121ξξξ=≤fL3.1ξ=x4.21,ξξ21,ξξ12ξξ≤21ξξ12ξξ≤1ξ2ξ()21,maxξξ=x.η()=∈=−.,0,...2,1],1,0[,1nxnxxfn[01]nξξξ...,,21()nxξξξ,...,,max21=.2)(xh)(xf]1,0[∈x)(xf()())()()()(xhxLgxhxLhxfLxf≡⋅=.L1)(≤xg1)()(max]1,0[=∈xhxfLx)(xg1[01]ξ)(xhhη2)(hgηξ≤13hηη=)(xfLE/1=−=2exp21)(2xxfπ()+∞−∞xπeL2≡,,(xexh−≡)()0+∞x,()}21exp{)(2−−≡xxg,()0+∞x.x()(xf),0+∞)0,(−∞),0(+∞)()()(xhxLgxf=1)(xh1lnξη−=hhη22ξ)(2hgηξ≤2ξ2ln2)1−≤(η−h3h)(x4hηeE2π=3.∫∞−=)(),()(xhdyyxgLxf),(yxg),(yx)(xhyL.1),(/1)(=∫∫+∞∞−∞−xhdxdyyxgL1(),(yxg),yxηη2()xyhηη≤13)(xfxηη=1L/x≤η()xyhηη≤xx≤η{}(){}(){}(){}xyxyxxyxhphxphxpxpηηηηηηηηη≤≤≤=≤≤=≤,()()()()()()122122112211111,,,dtdtttgLdtttgdtdtttgdtxththxth∫∫∫∫∫∫∞−∞−∞+∞−∞−∞−∞−==.(Bayes)x,y()()()ygxgyxg21,=()()()()12hxfxLgxgyd−∞=∫y.()10≤≤xh()21,[0,1]0,ygy∈=)()()(1xgxLhxf=[01]ξ[]2,0ππξδ2=δηcos==1)(xfπ=xy1ξ2ξ(g(1ξ2ξ(xg(g(fπ4=Lh−,01,112xx[01]1ξ2ξ22212221ξξξξ+−2221ξξ+=),()1(211yxhxy≡+=),()1(212yxhxy≡−=.),yxJyxhyxhfyx⋅=)),(),,((),211[01]1f1ξ,yx2ξ,(2x1))),((11=yhhf),y−=,0,10,1,141),2yxxyx.∫∞−=1),(4)dyyxgxπ.1)(=x1[01]1ξ2ξ22212221ξξξξ+−=x2221ξξ+=y211)(=≤xhy3φcos22212221ξξξξη+−=φsin2221212ξξξξη+=′φsinφsin785.0≈4=πE1[01]1ξ2ξ12,21−==ξξyx21122+yx3φcos2222yxyx+−=ηφsin222yxxy+=′ηφsinxy.dyyhyxgxf)()|()(∫+∞∞−=yx)|(yxg)(yhy)(yh|(hyxghy)|(hyxggx)dx)|(hyxgdxf≤ξf(yhy)()|fξhpnnp1=hn∑−=ni11≤ξ)x)fx=ξ.()(xxxpxxp+≤=+dxxdydxxg)(==∫+∞∞−)(xf1,,)()(xxfnn∑=,10∑nnp.np)(x1[0,1]ξ,n.∑=niiipp1(2),(hnnhηη=.,r,r01RR,3)(30312RRrrf−=10RrR≤≤.,[0,1]ξ,()[3/1303031RRR+−=ξη])(rf,,.001)(RxRRr+−=200121RRRR++=λ132)(33)()(200102201⋅+−+−=λλλRxRRRxRRxf.2.)()()(xgAxgAxf−=2211x[a,b],m,1212AA)(/)(xgxg)()(min12],[xgxgmbax∈=.−=)()()()(012211xgxgAAxgxf))((211mAAxg−≤.,021−mAA1)()()(0121≤−xgmAAxf)()()()()()(122122111211xgxgmAAAmAAAxgmAAxfxh−−−=−=,)(xf)()()()(1121xgxhmAAxf−=1)(01≤xh.)(1211mAAE−=,)(xf)()()(2221xgxhmmAAxf−=.mAAmAxgxgmAAmAxh212212112)()()(−−−=,01)(2≤xh.,1212)(mEmAAmE=−=.3,)()()(xgxHxfnnn∑=],[bax∈,(n=2).(n2)0)(≥xHnη)()()()()(2211xgxHxgxHxf+=.∫=badxxgxHp)()(111∫=badxxgxHp)()(222121=+pp)(xf)()()()()()()(221122221111xgpxgpxgpxHpxgpxHpxf′+′=+=.++++=)()()()()()(22221211121121xgMxHMMMxgMxHMMMMMxf.M[a,b]1212M)(xH)(xH2111MMMp+=2122MMMp+=.,2121MMLL+==)()(111xhMxH=,)()(222xhMxH=.[][])()()()()(22221111xgxhLpxgxhLpxf+=.,4)(xf,)()()()()(2211xgxHxgxHxf−=],[bax∈.)()()()(min1122],[xgxHxgxHmbax∈=,)(max1],[xHMbax∈=:)()1()1)(()()()()()(1)()()(01111112211xgmMmxgxHxgxHxgxHxgxHxf−≤−≤−=.−−=)()()()()1(1)(122111xgxgxHxHmMxh.)()()1()(xgxhmMxf−=1110,,1)(1≤xh)(xf)()(1)(222xgxhmmMxf−=.[a,b].2M)(2xH−−=)()()()()1()(221122xHxgxgxHmMmxh,)(2xh[a,b]1)(02≤xh.