概率论与数理统计公式汇总及重点详解(考研必备、期末必备-2013最新版)

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201212251,1à:‹öÊv‚‡)!(!nmmPnm-=)!(!!nmnmCnm-=BAABUBAII201212252WAUI¥=¥==11iiiiAABABAIU=BABAUI=WAA1A2A¥=¥==łŁ11)(iiiiAPAPUA{}n=WnPPPn1)()()(21==={})()()(21m)()()(21mPPP=A=)()()(W=LALAPB)()(APABP201212253=)/(ABP)()(APABPB)/()()(ABPAPABP=21(AAP)nA)|()|()(213121AAAPAAPAP=21|(AAAPn)1-nAAB)()()(BPAPABP=ABAB0)(AP)()()()()()()|(BPAPBPAPAPABPABP===ABABABABWnBBB,,,21LnBBB,,,21L),,2,1(0)(niBPiL=UniiBA1=)|()()|()()|()()(2211nnBAPBPBAPBPBAPBPAP+++=L1B2BnBA1B2BnB)(BiP=inUniiBA1=0)(AP==njjjiiiBAPBPBAPBPABP1)/()()/()()/()(iBP1=i2n)/(ABPi1=i2n201212254nuAAunAuAAnpAAqp=-1)(kPnnA)0(nkk££knkknnqpkPC-=)(nk,,2,1,0L=,Œà:ØÏÊvXXLLLL,,,,,,,,|)(2121kkkpppxxxxXPX=0‡kpL,2,1=k¥==11kkp)(xFX)(xfx¥-=xdxxfxF)()(X)(xfX0)(‡xf+¥¥-=1)(dxxfdxxfdxxXxPxXP)()()(»+£»=dxxf)(kkpxXP==)(201212255Xx)()(xXPxF£=)()()(aFbFbXaP-=£],(ba)(xF,1)(0££xF+¥¥-x)(xF21xx£)(1xF)(2xF0)(lim)(==-¥-¥fixFFx1)(lim)(==+¥+¥fixFFx)()0(xFxF=+)(xF)0()()(--==xFxFxXP£=xxkkpxF)(¥-=xdxxfxF)()(nApAXXn,,2,1,0LknkknnqpCkPkXP-===)()(nkppq,,2,1,0,10,1L=-=Xnp),(~pnBX1=nkkqpkXP-==1)(1.0=k201212256Xll-==ekkXPk!)(0lL2,1,0=kXl)(~lpXl),min(,2,1,0,)(nMllkCCCkXPnNknMNkM==•==--LL,3,2,1,)(1===-kpqkXPkX)(xfab-1-=,0,1)(abxfX~¥-==xdxxfxF)()(21,xxabxxxXxP--=1221)(0xa,abax--a1xba2012122570ll=+¥-p=+¥-=)(xf,xell-0‡x,0,0x,=)(xF,1xel--0‡x,,0x0201212258Xsmsp--=+¥¥-xm0sXms),(~2smNX)(xf)(xfm=xm=xspm21)(=f),(~2smNXXdtexFxt¥---=222)(21)(smps0=m1=s)1,0(~NX2221)(xex-=pj+¥¥-x¥--=Fxtdtex2221)(p)(xF21X),(2smNsm-X)1,0(NłŁ-F-łŁ-F=£smsm1221)(xxxXxPama)(£XPama)(XP201212259XLLLL,,,,,,,,)(2121nnipppxxxxXPX=)(XgY=)(iixgy=LLLL,,,,),(,),(),()(2121nnipppxgxgxgyYPY=)(ixgip)(ixg, àŒô:ØÏÊv1xxx),2,1,)(,(L=jiyxjix),(jiyx),2,1,()},(),{(L===jipyxYXPijjixMMMMMijpMMMMM.1=ijijp2012122510),(YX=x),)(,(+¥-¥+¥-¥yxyxf=˛DdxdyyxfDYXP,),(}),{(xx+¥¥-+¥¥-=.1),(dxdyyxf2)(),(yYxXyYxX=====Ixx3},{),(yYxXPyxF££=})(,)(|),{(2121yYxX£-¥£-¥),(0££yxF);0,(),(),,0(),(+=+=yxFyxFyxFyxF.1),(,0),(),(),(=+¥+¥=-¥=-¥=-¥-¥FxFyFF52121yyxx0)()()()(11211222‡+--yxFyxFyxFyxF.20121225114dxdyyxfdyyYydxxXxPyYxXP)()()(»+£+£»==5),2,1,()(L====•jipxXPPijjii),2,1,()(L====•jipyYPPijijj+¥¥-=dyyxfxfX),()(.),()(+¥¥-=dxyxfyfY6•===iijijppxXyYP)|(,)|(jijjippyYxXP•===)(),()|(yfyxfyxfY=)(),()|(xfyxfxyfX=7jiijppp••=,121),(2222121211221))((2)1(212œœßøŒŒºØłŁ-+---łŁ----=smssmmrsmrrspsyyxxeyxfr20121225128˛=,0),(1),(DyxSyxfD9,121),(2222121211221))((2)1(212œœßøŒŒºØłŁ-+---łŁ----=smssmmrsmrrspsyyxxeyxf1||,0,0,21,21rssmm).,,,2221,21rssmm).(~),,22,2211smsmNY)(~),,22,2211smsmNY201212251310Z=X+Y)()()(zYXPzZPzFZ£+=£=(P(X+Yz)=˛DdxdyyxfDYXP,),(}),{(dxxzxf+¥¥--),(222121,ssmm++=iiiCmm=iiiC222ssZ=max,min(X1,X2,Xn)nXXXL21,)()()(21xFxFxFnxxxLZ=max,min(X1,X2,Xn))()()()(21maxxFxFxFxFnxxxL•=)](1[)](1[)](1[1)(21minxFxFxFxFnxxx--•--=L20121225142cnXXX,,,21L==niiXW12‡łŁG=--.0,0,0221)(2122uueunufunn2c)(2nc.2012dxexnxn-¥+-=łŁG2c),(2iinYc-).(~2112kkiinnnYZ+++==Lct),(~),1,0(~2nYNXcnYXT/=2121221)(+-łŁ+łŁGłŁ+G=nntnnntfp).(+¥-¥t)()(1ntntaa-=-2012122515F)(~),(~2212nYnXcc21//nYnXF=‡łŁ+łŁłŁGłŁGłŁ+G=+--0,00,1222)(2211222121212111yyynnynnnnnnyfnnnn),(1),(12211nnFnnFaa=-,Ûà:ØτpWy1kxX===nkkkpxXE1)(+¥¥-=dxxxfXE)()(==nkkkpxgYE1)()(+¥¥-=dxxfxgYE)()()()()(XDX=s-=kkkpXExXD2)]([)(+¥¥--=dxxfXExXD)()]([)(22012122516iikipxkm.))((kkXEXE-=m-iikipXEx))((+¥¥-,)(dxxfxkkm.))((kkXEXE-=m+¥¥--,)())((dxxfXExk22)(esem£‡-XP)(em‡-XP2===niniiiiiXECXCE11)()(201212251734),1(pB)1(pp-),(pnB)1(pnp-)(lPll)(pGp121pp-),,(NMnHNnMłŁ--łŁ-11NnNNMNnM),(baU2ba+12)(2ab-)(lel121l),(2smNm2s2c2-nn5=•=niiipxXE1)(=•=njjjpyYE1)(+¥¥-=dxxxfXEX)()(+¥¥-=dyyyfYEY)()()],([YXGEijijjipyxG),()],([YXGE+¥¥+¥¥dxdyyxfyxG),(),(2012122518•-=iiipXExXD2)]([)(•-=jjjpYExYD2)]([)(+¥¥--=dxxfXExXDX)()]([)(2+¥¥--=dyyfYEyYDY)()]([)(211m),cov(YXXYs))].())(([(11YEYXEXEXY--==msXYsXXsYYs)()(YDXDXYsXYrrrr1)(=+=baYXP-==)0(1)0(1aarr0=r0=XYrłŁYYYXXYXXssss2012122519)(lkYXEkln].))(())([(lkklYEYXEXEu--=6(iv)70=XYrrssmm,,,,222121,”à'pš‹Œ-ÁPš1mfiX.1)(11lim11=łŁ-==¥fieniiniinXEnXnP.11lim1=łŁ-=¥fiemniinXnP.1lim=łŁ-¥fiempnPn.0lim=łŁ‡-¥fiempnPn.11lim1=łŁ-=¥fiemniinXnP20121225202),(2nNXsmfi),2,1(0)(,)(2L=„==kXDXEkksmsmnnXYnkkn=-=1¥--=¥fi¥fi=£-=xtnkknnndtexnnXPxF.21lim)(lim212psmnX¥--¥fi=£--=xtnndtexpnpnpXP.21)1(lim22p3),(,knpNMNfi¥fiknkknnNknMNkMppCCCC----fi)1().(¥fiN40,fi¥filnpnll--fi-ekppCkknkkn!)1().(¥fin,mà7,ʽ712012122521nxxx,,,21Lnxxx,,,21Lnxxx,,,21Lnxxx,,,21Ljj=nxxx,,,21Ljjjnxxx,,,21L===--=niixxnS122.)(11.)(1112=--=niixxnS===nikikkxnM1.,2,1,1L==-=¢nikikkxxnM1.,3,2,)(1Lm=)(XEnXD2)(s=22)(s=SE221)*(snnSE-==-=niiXXnS122)(1*20121225222nxxx,,,21L),(2smN).1,0(~/Nnxudefsm-tnxxx,,,21L),(2smN),1(~/--ntnsxtdefm2cnxxx,,,21L),(2smN--cs)1(2-nc2c=--=uE=u=u-+-=-==cs--=-c2012122523Fnxxx,,,21L),(21smNnyyy,,,21L),(22smN),1,1(~//2122222121--nnFSSFdefss,)(11211211=--=niixxnS;)

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