教案2§2——统计概念

1、统统 计计 概概 念念重庆大学数统学院重庆大学数统学院 李寒宇李寒宇240783951240783951135942309691359423096912(,)|,1,2,nix xxxR in ( )F x),(),(221121nnnxXxXxXPxxxFniiniiixFxXP11)()(niRxi, 2 , 1,)(xfniinxfxxf11)(),(),1,2,iP Xxi其它当，0)()(,.2 , 1,iixxixXPxfniinxfxxxf121)(),(niinxfxxf11)(),(,0( )00 xexf xx，niinxfxxxf121)(),(nixeeeixnnxnn

2、ixniii, 1, 0,)(11niixnx11(1,)XBp),(21nXXX1(1),0,1,01( )0 xxppxpf x其它，niinxfxxxf121)(),(nixppixnnxn, 1, 1 , 0,)1 (niiniiiixxnixxpppp11)1 (11)1 ()1 (),(21nXXX),(1nxxfnxx,1nxx,1),(1nXXfniiXnX11;)(11122niiXXnS, 2 , 1;11kXnMnikik, 2 , 1;)(11*kXXnMnikik;)(1112niiXXnSXM 12*21SnnM)(111222niiXnXnSX0)(1niiXX0

3、)(111XnXnXXXXniniinii2,EXDX2,EXDXnnnXEnXnEXEniinii1)(1)1(11nnnXDnXnDXDniinii2221211)(1)1(pX)(2XDES )(1*2XDnnEM)(XD2211()()nniiiixxxa222221111()1111nniiiinnESEXXEXEXnnnn2222()() )111nnnEXEXDXEXDXEXnnn22()() )1nDXDXEXEXDXnn ),(1nxx )()2()1 (nxxx)(iXnixi, 2 , 1,)()()2()1(,nXXX12(,)nXXX)1 (X)(nX*( )(1)n

4、nRXX为偶数时当，为奇数时当n21n,)12()2()21(nnnXXXX)(xf)(xF)(nX)()()()(xXPxFnn)()()(1)(xfxFnxfnn)1(X)()()1()1(xXPxF)()(1)(1)1 (xfxFnxfn),(1xXxXPnnxF)()(1)1(xXPnxF)(11),(11xXxXPn),(51XX (12,9)N18),max(51XXP51,XX (12,9)N18),max(118),max(5151XXPXXP1089. 0)9772. 0(1)2(1312181)18(118118,181555515151XPXPXXPii1089. 031

5、2181)18(118),max( 5)5(51FXXP或：9),min(51XXP)9),(min(51XXP5785. 0)8413. 0(1)1 (1)1(1 1312911)9(1)9, 9(155555151XPXXP5785. 0312911)9()9),(min( 5)1(51FXXP或：)9),(min(151XXPnxxx,21)()2()1(nxxx(1)( )(1)( )0, ( ), ;1,2,11, nkknxxkF xxxxknnxx其中)(xFn)1(x)2(x)(nxoooo)(xFnx图1 经验分布函数曲线)(xFn)(xFn1)(0 xFn()1,()0nn

6、FF )()0(xFxFnn)(xFn)(xFn),(21nXXXTnXXX,21) 1 , 0(NniiX1222)(22n/2 1/2/21,02( /2)( )0,0nxnxexnf xx22( )n2En22Dn2211()n2222()n2122)(2122221nn ) 1 , 0( NX) 1 (22X1,nXX2( ,)N 2211()niiSXn222( )nSn42222,ESDSn,1,.,iiXYin1,nYY(0,1)N222222221111()()( )nnniiiiiiXnSYXn2222(),()2nSnSEnDn42222,ESDSn)(),1 , 0(2n

7、YNXnYXT )(ntT1221()2( )(1),( /2)nnxf xxRnnn2nDTn211( ),1f xxRx221( ),2xf xexR)(),(22nYmXnYmXF ),(nmFF/2/2 12()2()(1),0( )(/2) ( /2)0,0n mmmmnmmxxxf xmnnnx(2) 密度函数：(4) 性质：当 时，则 ；( , )FF m n);,(1mnFF当，则 ； ( )Tt n2(1, )TFn(3) 密度函数曲线：1234,XXXX2(0,2 )N2211234(2)(34)Ya XXbXX1222234XXYcXX24232213)2(XXXXdY，

8、1Y22Y3Y122(0,20)XXN3434(0,100)XXN1234,XXXX2(0,2 )N，12220XX343410XX)2(10432022243221XXXX1001,201ba)2 , 0(),2 , 0(2423NXNX)8 , 0(21NXX ) 1 , 0(821NXX ) 1 , 0(2),1 , 0(243NXNX)2()(4122224232423XXXX)2(2)(418/ )(242321242321tXXXXXXXX1222234 (2)XXYtXX ，且自由度为1和2。) 1 (2022221 XX2223421() (2)2XX )2 , 1 (2211

9、20224232221FXXXX52d2( ,)XN 2,X S2( ,)XNn(0,1)/XNn222(1)(1)nSn2XS与1,nXX2( ,)N (1)/XTt nSn222(1)(0,1),(1)/XnSNnn2XS与21(,)N 22(,)N 1222()(2) (2)XYXYmn mnTt mnmnmSnS22(1,1)XYSFF mnSpvpXPFpp)()(pvpvpuppuu1pupu概率ppppppppuuuXPpuXPpuXPuXPuXPp11)(1)(1)(1)()(所以：又?95. 0u65. 195. 0u?28. 0u58. 072. 028. 0128. 0uuu)(ntppupt概率p)()(1ntntpp?)8(975. 0t306. 2)8(975. 0t22)(2np),(mnFpppunt)(221( )(21)2ppnun11( , )( ,)ppF m n