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=maxx-minxRbnkh.khR/knk50~100101~200201~500501~10007~98~109~1110~15cdin,nnfii=eiihf/fiF-2-xMe~xModRnn-12sixxix-xix-xixn0nn-1cvcv=s/xΩa)b)Ω-3-ABC5aAΩbAA1ω2ωΩ1ω1ωA2ω2ωcAdΩΩΩeΩφa,ΩAΩ−AbABABABAUBcABABAABA−A-4-BABABdABABABA-B1m2mkm1mX2mXXkm1m2mkm1m+2mkm)1()1(+−××−×rnnnLrnpnp!),1()1(nprnnnpnrn=+−−=LrnABBA-5-)(nrr≤)!(!!!)1()1(!rnrnrrnnnrprnrn−=+−−==⎟⎟⎠⎞⎜⎜⎝⎛L10=⎟⎟⎠⎞⎜⎜⎝⎛na)Ab)nAknAfn(A)=kn/n=A/fn(A)Afn(A)An01A:0P(A)01P(Φ)=0P(Ω)=1−AP(A)+P(−A)=1P(−A)=1-P(A)ABP(A-B)=P(A)-P(B)ABP(AUB)=P(A)+P(B)-P(AB)ABP(AB)=P(Φ)=0P(AUB)=P(A)+P(B)A1A2A3…LLUUU+++=)()()()(321321APAPAPAAAP…ABP(AB)=P(AB)P(B)=P(B)P(A)P(B)0,P(A)0ABAB-6-P(AB)=P(A)P(B)ABBAP(AB)AP(A)P(AB)=P(AB)/P(B)=P(A)P(B)/P(B)=/P(A)AB,BAP(AB)P(AB)=P(AB)/P(B)P(B)0ABABXnxxx,,,21Lnppp,,,21LPX=ix=ipi=1,2,3,…,nipip121=+++npppLip2a)XabE(aX+b)=aE(X)+bVar(aX+b)=a2Var(X)b)1X2X)()()(2121XEXEXXE+=+c)1X2X)()()(2121XVarXVarXXVar+=±bc-7-E(X)E(X)=∑iiipxE(X)=∫baxp(x)dxVar(X)Var(X)=[]∑−iiipXEx2)(Var(X)=[]∫−badxxpXEx)()(2XXσ)()(XVarX==σσ3NMnXMn≤Xn,,1,0LMnXM,,1,0LX=xrxnNxnMNxMxXPL,2,1,)(=⎟⎟⎠⎞⎜⎜⎝⎛⎟⎟⎠⎞⎜⎜⎝⎛−−⎟⎟⎠⎞⎜⎜⎝⎛==),,min(Mnr=),,(MNnhNnMXE=)(⎟⎠⎞⎜⎝⎛−•−−=NMNMNnNnxVar11)()(Xp(x)f(x)-8-xp(x)Xxp(x)abnnp,1-pXnX01nn+1xnxPPxnxXP−−⎟⎟⎠⎞⎜⎜⎝⎛==)1()(nxexXPxx,...1,0,)(!===−λλnpXE=)(λ=)(XE)1()(pnpxVar−=λ=)(xVar)1()(pnpx−=σλσ=)(xcµσµσµµσσσσauauau-9-1),(~2σµNX)10(~NXUσµ−=σµ−X2),(~2σµNX)()(σµ−Φ=bbXP)(1)(σµ−Φ−=aaXP)()()(σµσµ−Φ−−Φ=abbXaP)(•Φµσa⎩⎨⎧≥=−0,00,)(xxexpxλλ)(λExpλ0E(X)=1/λ-10-2/1)(λ=XVarbXYln=}{2/exp)(2YYXXEσµµ+==}1){exp()(222−==YXXXVarσµσX1,X2,….XnnnXN(),2nσµxx2σxX2)(11)(∑−−−=−XXnXnnsXiµµ-11-2χ2σ2χ2χ()())1(~/1222122−−=−∑=nXXsnniiχσσ2χ21,σµ22,σµX1,X2,….Xn21,σµ1,Y2,….Ym22,σµ()())1,1(~111112122221−−−−−−=∑∑==mnFYYmXXnssmiiniin-1m-1FθXnX1,X2,….Xnθθˆˆ=X1,X2,….XnθˆθθˆθX1,X2,….Xnθˆθxµ2s2σs-12-λ1)(=XE)(/1XE=λx)(XEx/1ˆ=λxx=λˆXp=ˆ1µxx~)...(1ˆ21nxxxnx+++==µxµ22σ2s∑=−−==niixxns1222)(11ˆσ3σ())1(xxRn−=s()2)1()(2//ˆdxxdRnR−==σ∑=−−==ninscxxncs1424/)(11/ˆσσsσˆRσˆsσˆθΘnnxxx,...,,21)10(aa),...,,(21nLLxxxθθ=),...,,(21nUUxxxθθ=Θ∈θaPUL−≥≤≤1)(θθθ[]ULθθ,θ1-a[]ULθθ,θ1-aLθUθ1-a-13-1-a[]ULθθ,θ1-a2/)()(aPPUL==θθθθp1-aµσnuxaσ2/1−±µσnsntxa)1(2/1−±−2σµ⎥⎦⎤⎢⎣⎡−−−−−)1()1(,)1()1(22/222/12nsnnsnaaχχσµ⎥⎥⎦⎤⎢⎢⎣⎡−−−−−)1(1,)1(122/22/1nnsnnsaaχχnxxuxa/)1(2/1−±−2/1au−1-a/2a0H0Hµµ::01HH≠bσ0H)1,0(~/00Nnxuσµ−=uc0HWW={|u|c}c-14-0HW0H0HW0HdWN2/au2/1au−2/au2/1au−W={2/au2/1au−}={2/1au−}enxxx,...,,21W0H1Hnxxx,...,,21W0H0H1Hσµ0µµ0µµ=0µµ0µµ0µµ0µnxu/0σµ−=}{1auu−}{auu}|{|2/1auu−tσµ0µµ0µµ=0µµ0µµ0µµ0µnsxt/0µ−=)}1({1−−ntta)}1({−ntta)}1(|{|2/1−−ntta2χµ2σ20σ2σ20σ2σ20σ2σ20σ2σ20σ2σ20σ2022)1(σχsn−={)1(212−−naχχ}{)1(22/2−naχχ}{)1()1(22/1212/2−−−nnaaχχχχ}-15-pa0H1Hup0pp0pp0pp0pp0pp0pnpppxu/)1(000−−={auu−1}{auu}{2/1||auu−}-16-2131-17-61313265-18-C.0+D.[0+]∑==niixnX11)2250004000524000300012230002000142200010007210000(401×++×++×++×++×+×-19-2sxsxxs2xsxxxx95.021.01212.044.0uxuxnux±=±=±−−σα-20-nuxσα21−±96.1,5.0975.0==uσ221×−nuσαxxxn2σx40410)(2=×=×=xVarnσZαZα−1Z2αZ21α−Z2α-21-21α−u11136136253611⊃AB)()()|(BPABPBAP=⊃-22-)(,21)(4)3(2〈+∞−∞〈=+−xexpxπ23+X23+X23−X23−X)(,21)(222)(〈+∞−∞〈=−−xexpxσµσπ23+=−=XXUσµ⎟⎟⎠⎞⎜⎜⎝⎛−Φ=〈=〈=〈YYaaYPaXPaXPσµln)ln()ln(ln)(()()()7157.05656.025460ln460,2)(,5ln=Φ=⎟⎠⎞⎜⎝⎛−Φ=〈====XPXVarXEYYσµ-23-142===nsσ())()(YVarXVarYX+=±σ-24-)(,)(nnppxXEiiiii==∑()()156102010152102020158)(=+×++×=XEnuxσα21−±96.1,3975.0==uσ221×−nuσα-25-∑==niixnX1161()21211∑=−−=niixxnS()()1xxRn−=⎥⎦⎤⎢⎣⎡+=+12221~nnxxx-26-)0)((,)()()|(〉=BPBPABPBAP-27--28-xxxxxxxxx-29-()∑∑==−−==niiniixnsxnxx122111,1x16,5.2,10232221===SSS()∑=−−niixnx1211⎥⎥⎦⎤⎢⎢⎣⎡−−∑=niixnx12211⎥⎦⎤⎢⎣⎡−−∑=niixnnx12211⎥⎥⎦⎤⎢⎢⎣⎡⎟⎠⎞⎜⎝⎛−−∑∑==niniiixxnn1212111σµ−X1-30-D.AB-31--32-5.1!5.1−eXxλλ−eXx!⎟⎠⎞⎜⎝⎛−Φ=σµLSLPL⎟⎠⎞⎜⎝⎛−Φ−=σµLSLPL1⎟⎠⎞⎜⎝⎛−Φ=σµUSLPU⎟⎠⎞⎜⎝⎛−Φ−=σµUSLPU1()⎟⎠⎞⎜⎝⎛−Φ=〈=σµLLLTTXPP()⎟⎠⎞⎜⎝⎛−Φ−=〉=σµUUUTTXPP1-33-θˆθθˆθˆθθˆθθˆθˆθˆθθˆθθˆθθˆX-34-XXXX34X916X-35-X-36-96.102.29015.05.0511.021=〉=−=−=−ασµunxu0098.0511.09015.096.1511.021±=×±=±−nuxσα-37-3Y=5000(13-X)××41011120.50.40.1-38-C.2500D.3000-39-1ABC1Ai22σ3ijyrHµµµ===L210:rHµµµ,,,:211LrH0AA2Armimiiyyy,,,21Li=1,2,..,riiyyTiiTnn=rmn()∑∑∑∑====−=−=ririmjijmjijTnTyyyS1121212AA()nTmTyymSriiriiA21212−=−=∑∑==-40-()∑∑==−=rimjiijeyyS112ST=SA+SeSTSASefTfAfefT=fA+fefT=n-1=rm-1,fA=r-1,fe=fT-fA=r(m-1)VA=SA/fAVe=Se/feFF=VA/Ve1ATiT2∑∑∑222TTyiij3STSASe4F5αFFF1-αfAfeFF1-αfAfeAA3FAeSASefA=r-1fe=n-r)VA=SA/fAVe=Se/feF=VA/VeTSTfT=n-1x,ynr1r=0nr0r0-41-rnr()()()()yyxxxyiiiiLLLyyxxyyxxr=−−−−=∑∑∑22()()()()∑∑∑−=−=−−=22yyLxxLyyxxLiyyixxiixyρH0ρ=0H1ρ0(){}22/1−=−nrrWαnα3bxay+=ˆxbyaLLbxxxy−==,/bar=10r1r=0r=0-1r0r=-1-42-αrr1-a/2(n-2)()∑−=2yySiTxxy()∑−=2ˆyySiRx()∑−=2ˆiiEyySST=SR+SEfT=fR+fEfT=n-1,fR=1,fE=fT-fRFEERRfSfSF//=αFF1-α(fR,fE)4yxx0y00ˆbxay+=1-αy()δδ+−00ˆ,ˆyyδ{}αδ−=−10yyPxxLxxnnt/)(/11)2(ˆ202/1−++−=−ασδyL,yUxULyubxayubxa++−+−−σσααˆˆ2121x1-α5n-43-Ln(qp)npq[L423]n=qk,k=2,3,4,…p=(n-1)/(q-1)[L12211]123-44-4S-fVeSTfTVe/ST1−≤nn-45-eASS29eASS92AeSS29AeSS92AeeAeeAAfSfSfSfSF==yˆ-46--47-iiyx,bxay+=ˆiibxay+=ˆ()21ˆ∑=−niiiyyiyy()211∑∑==−rimjijyy()211∑∑==−rimjiijyy()21∑=−riiyy()21∑=−riiyym-48-7.440.12030.423===eeAAfSfSF-49-12315,21,15456=−=−==−==