5 参数估计(二).pdf

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1、?3.?4.?MLE?MLE?MLE?MLE?1?2MLE?3MLE?MLE?MLE?1.?MLE?MLE?1?3?3?1?(1)?1=1/4?2=3/4.?A?“?”.?,?P(A)=,1,2.?1 2?2.?MLE?MLE?1?3?3?1?(1)?1=1/4?2=3/4.?A?“?”.?,?P(A)=,1,2.?1 2?2.?MLE?MLE?1?3?3?1?(1)?1=1/4?2=3/4.?A?“?”.?,?P(A)=,1,2.?1 2?2.?MLE?MLE?1?3?3?1?(1)?1=1/4?2=3/4.?A?“?”.?,?P(A)=,1,2.?1 f(2)=364?.?1.?MLE?M

2、LE?(2)?B?,?P(B)=(1 )2 f(),1,2?f(1)=964 f(2)=364?.?1.?MLE?MLE?(2)?B?,?P(B)=(1 )2 f(),1,2?f(1)=964 f(2)=364?.?1.?MLE?MLE?(2)?B?,?P(B)=(1 )2 f(),1,2?f(1)=964 f(2)=364?.?1.?MLE?MLE?(2)?B?,?P(B)=(1 )2 f(),1,2?f(1)=964 f(2)=364?.?1.?MLE?MLE?,?.?X1,Xn?x1,xn?L()=L(|x1,xn),.L()?(x1,xn)?L()?.=(X1,Xn)?MLE?MLE?

3、MLE?,?.?X1,Xn?x1,xn?L()=L(|x1,xn),.L()?(x1,xn)?L()?.=(X1,Xn)?MLE?MLE?MLE?,?.?X1,Xn?x1,xn?L()=L(|x1,xn),.L()?(x1,xn)?L()?.=(X1,Xn)?MLE?MLE?MLE?,?.?X1,Xn?x1,xn?L()=L(|x1,xn),.L()?(x1,xn)?L()?.=(X1,Xn)?MLE?MLE?MLE?.?i?Xi=1?Xi=0,?L()=nYi=1xi(1 )1xi=P3k=1xk(1 )3P3k=1xk.?(0,1,0),?P3k=1xk=1,?L()=(1 )2.?=1,

4、2.=1?L()?=1?MLE?MLE?MLE?.?i?Xi=1?Xi=0,?L()=nYi=1xi(1 )1xi=P3k=1xk(1 )3P3k=1xk.?(0,1,0),?P3k=1xk=1,?L()=(1 )2.?=1,2.=1?L()?=1?MLE?MLE?MLE?.?i?Xi=1?Xi=0,?L()=nYi=1xi(1 )1xi=P3k=1xk(1 )3P3k=1xk.?(0,1,0),?P3k=1xk=1,?L()=(1 )2.?=1,2.=1?L()?=1?MLE?MLE?MLE?X1,Xn?x1,xn?(1)?:L()=nYk=1P(Xk=xk;)(2)?:L()=nYk=1p

5、(xi;).?L()?.?.?.?L()=maxL()?MLE.?MLE?MLE?X1,Xn?x1,xn?(1)?:L()=nYk=1P(Xk=xk;)(2)?:L()=nYk=1p(xi;).?L()?.?.?.?L()=maxL()?MLE.?MLE?MLE?2.MLE?MLE?MLE?MLE?k?=(1,2,k).?l()=lnL()?L()?l()?.?l()i=0,i=1,2,k.?.?MLE.?MLE?MLE?MLE?k?=(1,2,k).?l()=lnL()?L()?l()?.?l()i=0,i=1,2,k.?.?MLE.?MLE?MLE?MLE?k?=(1,2,k).?l()=

6、lnL()?L()?l()?.?l()i=0,i=1,2,k.?.?MLE.?MLE?MLE?MLE?k?=(1,2,k).?l()=lnL()?L()?l()?.?l()i=0,i=1,2,k.?.?MLE.?MLE?MLE?MLE?k?=(1,2,k).?l()=lnL()?L()?l()?.?l()i=0,i=1,2,k.?.?MLE.?MLE?MLE?p(?)?n?T?p?.?b(1,p).?x1,xn,?Pnk=1xk=T.?(1)?L(p)=nYk=1pxk(1 p)1xk=pPnk=1xk(1 p)nPnk=1xk.(2)?l(p)=nXk=1xklnp+?n nXk=1xk?l

7、n(1 p).?MLE?MLE?p(?)?n?T?p?.?b(1,p).?x1,xn,?Pnk=1xk=T.?(1)?L(p)=nYk=1pxk(1 p)1xk=pPnk=1xk(1 p)nPnk=1xk.(2)?l(p)=nXk=1xklnp+?n nXk=1xk?ln(1 p).?MLE?MLE?p(?)?n?T?p?.?b(1,p).?x1,xn,?Pnk=1xk=T.?(1)?L(p)=nYk=1pxk(1 p)1xk=pPnk=1xk(1 p)nPnk=1xk.(2)?l(p)=nXk=1xklnp+?n nXk=1xk?ln(1 p).?MLE?MLE?p(?)?n?T?p?.?b

8、(1,p).?x1,xn,?Pnk=1xk=T.?(1)?L(p)=nYk=1pxk(1 p)1xk=pPnk=1xk(1 p)nPnk=1xk.(2)?l(p)=nXk=1xklnp+?n nXk=1xk?ln(1 p).?MLE?MLE?(?)(3)?l(p)=1pnXk=1xk11 p?n nXk=1xk?=0.(4)?p=1nnXk=1xk=x.(5)?l(x)0,?p=x?l(p)?(6)?p=X=T/n?p?MLE.?MLE?MLE?(?)(3)?l(p)=1pnXk=1xk11 p?n nXk=1xk?=0.(4)?p=1nnXk=1xk=x.(5)?l(x)0,?p=x?l(p

9、)?(6)?p=X=T/n?p?MLE.?MLE?MLE?(?)(3)?l(p)=1pnXk=1xk11 p?n nXk=1xk?=0.(4)?p=1nnXk=1xk=x.(5)?l(x)0,?p=x?l(p)?(6)?p=X=T/n?p?MLE.?MLE?MLE?(?)(3)?l(p)=1pnXk=1xk11 p?n nXk=1xk?=0.(4)?p=1nnXk=1xk=x.(5)?l(x)0,?p=x?l(p)?(6)?p=X=T/n?p?MLE.?MLE?MLE?X1,Xn?X1,Xn?N(,2).?=(,2).?L()=nYk=1(22)12expn(Xi)222o=(22)n2exp

10、nPni=1(Xi)222o.l()=n2ln(22)Pni=1(Xi)222.?MLE?MLE?X1,Xn?X1,Xn?N(,2).?=(,2).?L()=nYk=1(22)12expn(Xi)222o=(22)n2expnPni=1(Xi)222o.l()=n2ln(22)Pni=1(Xi)222.?MLE?MLE?X1,Xn?X1,Xn?N(,2).?=(,2).?L()=nYk=1(22)12expn(Xi)222o=(22)n2expnPni=1(Xi)222o.l()=n2ln(22)Pni=1(Xi)222.?MLE?MLE?X1,Xn?X1,Xn?N(,2).?=(,2).?L

11、()=nYk=1(22)12expn(Xi)222o=(22)n2expnPni=1(Xi)222o.l()=n2ln(22)Pni=1(Xi)222.?MLE?MLE?X1,Xn?X1,Xn?N(,2).?=(,2).?L()=nYk=1(22)12expn(Xi)222o=(22)n2expnPni=1(Xi)222o.l()=n2ln(22)Pni=1(Xi)222.?MLE?MLE?(?)?l()=2nXi=1(Xi)=0l()2=n22+124nXi=1(Xi)2=0?=X,2=1nnXi=1(XiX)2=S2n.?l()?=(,2)?MLE.?MLE?MLE?(?)?l()=2nX

12、i=1(Xi)=0l()2=n22+124nXi=1(Xi)2=0?=X,2=1nnXi=1(XiX)2=S2n.?l()?=(,2)?MLE.?MLE?MLE?(?)?l()=2nXi=1(Xi)=0l()2=n22+124nXi=1(Xi)2=0?=X,2=1nnXi=1(XiX)2=S2n.?l()?=(,2)?MLE.?MLE?MLE?MLE?MLE?.?X1,Xn?U(0,).?MLE?L()=1n,X(n).?X(n),+)?L()=1n L(X(n)=1Xn(n).?X(n)?MLE?MLE?MLE?MLE?MLE?.?X1,Xn?U(0,).?MLE?L()=1n,X(n).?

13、X(n),+)?L()=1n L(X(n)=1Xn(n).?X(n)?MLE?MLE?MLE?MLE?MLE?.?X1,Xn?U(0,).?MLE?L()=1n,X(n).?X(n),+)?L()=1n L(X(n)=1Xn(n).?X(n)?MLE?MLE?MLE?MLE?MLE?.?X1,Xn?U(0,).?MLE?L()=1n,X(n).?X(n),+)?L()=1n L(X(n)=1Xn(n).?X(n)?MLE?MLE?MLE?MLE?MLE?.?X1,Xn?U(0,).?MLE?L()=1n,X(n).?X(n),+)?L()=1n L(X(n)=1Xn(n).?X(n)?MLE?

14、MLE?MLE?3.MLE?MLE?MLE?MLE?MLE?MLE.g()?g(MLE)?g()?MLE.?X1,Xn?X N(,2).?2?MLE?=X,2=S2n.?MLE?Sn.?P(X 3)=?3?MLE?3XSn?.?0.9?x0.9=+u0.9?MLE?X+u0.9Sn.?u=1().?MLE?MLE?MLE?MLE?MLE.g()?g(MLE)?g()?MLE.?X1,Xn?X N(,2).?2?MLE?=X,2=S2n.?MLE?Sn.?P(X 3)=?3?MLE?3XSn?.?0.9?x0.9=+u0.9?MLE?X+u0.9Sn.?u=1().?MLE?MLE?MLE?ML

15、E?MLE.g()?g(MLE)?g()?MLE.?X1,Xn?X N(,2).?2?MLE?=X,2=S2n.?MLE?Sn.?P(X 3)=?3?MLE?3XSn?.?0.9?x0.9=+u0.9?MLE?X+u0.9Sn.?u=1().?MLE?MLE?MLE?MLE?MLE.g()?g(MLE)?g()?MLE.?X1,Xn?X N(,2).?2?MLE?=X,2=S2n.?MLE?Sn.?P(X 3)=?3?MLE?3XSn?.?0.9?x0.9=+u0.9?MLE?X+u0.9Sn.?u=1().?MLE?MLE?MLE?p(x,),?MLE?MLE.?MLE?.?n?n(MLE)

16、?N(0,V(),?V()=hE?lnp(x,)?2i1.?MLE?MLE?MLE?p(x,),?MLE?MLE.?MLE?.?n?n(MLE)?N(0,V(),?V()=hE?lnp(x,)?2i1.?MLE?MLE?5.3(?305?)?1?2?4?5?8?1?2?3?4?5?1.?X1,Xn?(0,1)?L?U?P(L U)1 ,.?L,U?1?L?U?“?1 ”?100(1 )%?.?=15.?10?14.8513.0113.5014.9316.9713.8017.9513.3716.2912.38?90%?13.6247,15.7679?=15.?100?100?100?.?“?1

17、”?100(1 )%?.?=15.?10?14.8513.0113.5014.9316.9713.8017.9513.3716.2912.38?90%?13.6247,15.7679?=15.?100?100?100?.?“?1 ”?100(1 )%?.?=15.?10?14.8513.0113.5014.9316.9713.8017.9513.3716.2912.38?90%?13.6247,15.7679?=15.?100?100?100?.?“?1 ”?100(1 )%?.?=15.?10?14.8513.0113.5014.9316.9713.8017.9513.3716.2912.3

18、8?90%?13.6247,15.7679?=15.?100?100?100?.?90%?Figure:?90%?100?91?9?50%?Figure:?50%?50%.?100?50?50?2.?X1,X2,Xn?N(,1).?X.X?N(,1/n),?T(X,)=n(X )N(0,1)=P(|T(X,)|u1/2)=1 .?u1=1(1 ).?|T(X,)|u1/2?X u1/2/n X+u1/2/n?1?X1,X2,Xn?N(,1).?X.X?N(,1/n),?T(X,)=n(X )N(0,1)=P(|T(X,)|u1/2)=1 .?u1=1(1 ).?|T(X,)|u1/2?X u1

19、/2/n X+u1/2/n?1?X1,X2,Xn?N(,1).?X.X?N(,1/n),?T(X,)=n(X )N(0,1)=P(|T(X,)|u1/2)=1 .?u1=1(1 ).?|T(X,)|u1/2?X u1/2/n X+u1/2/n?1?X1,X2,Xn?N(,1).?X.X?N(,1/n),?T(X,)=n(X )N(0,1)=P(|T(X,)|u1/2)=1 .?u1=1(1 ).?|T(X,)|u1/2?X u1/2/n X+u1/2/n?1?,?(1)?G(,),?G(,)?G(,)?.(2)?c?d?P(c G(,)d)1 .(3)?:c G(,)d=L,U?L,U?1?.

20、?,?(1)?G(,),?G(,)?G(,)?.(2)?c?d?P(c G(,)d)1 .(3)?:c G(,)d=L,U?L,U?1?.?,?(1)?G(,),?G(,)?G(,)?.(2)?c?d?P(c G(,)d)1 .(3)?:c G(,)d=L,U?L,U?1?.?,?(1)?G(,),?G(,)?G(,)?.(2)?c?d?P(c G(,)d)1 .(3)?:c G(,)d=L,U?L,U?1?.?X1,X2,Xn?N(,2),?2?(1 )?.?T(X,)=n(X )/N(0,1)?T(X,)?,?1 =P(u12 T(X,)u12)=P(X u12/n X+u12/n)?1?

21、X u12/n X+u12/n?X1,X2,Xn?N(,2),?2?(1 )?.?T(X,)=n(X )/N(0,1)?T(X,)?,?1 =P(u12 T(X,)u12)=P(X u12/n X+u12/n)?1?X u12/n X+u12/n?X1,X2,Xn?N(,2),?2?(1 )?.?T(X,)=n(X )/N(0,1)?T(X,)?,?1 =P(u12 T(X,)u12)=P(X u12/n X+u12/n)?1?X u12/n X+u12/n?X1,X2,Xn?N(,2),?2?(1 )?.?T(X,)=n(X )/N(0,1)?T(X,)?,?1 =P(u12 T(X,)u1

22、2)=P(X u12/n X+u12/n)?1?X u12/n X+u12/n?X1,X2,Xn?N(,2),?2?(1 )?.?T(X,)=n(X )/N(0,1)?T(X,)?,?1 =P(u12 T(X,)u12)=P(X u12/n X+u12/n)?1?X u12/n X+u12/n?X1,X2,Xn?N(,2),?2?(1 )?.?T(X,)=n(X )/N(0,1)?T(X,)?,?1 =P(u12 T(X,)u12)=P(X u12/n X+u12/n)?1?X u12/n X+u12/n?1 =P(uan(X )/ub)=P(X+ua/n X+ub/n)?0 a b 1?b

23、a=1?.?a=/2,b=1 /2.?1 =P(uan(X )/ub)=P(X+ua/n X+ub/n)?0 a b 1?b a=1?.?a=/2,b=1 /2.?1 =P(uan(X )/ub)=P(X+ua/n X+ub/n)?0 a b 1?b a=1?.?a=/2,b=1 /2.?1 =P(uan(X )/ub)=P(X+ua/n X+ub/n)?0 a b 1?b a=1?.?a=/2,b=1 /2.?3.?X1,X2,Xn?N(,2)?1?(1)2?;(2)2?;(3)?2?;(4)?2?.?(2?)?n(X )N(0,1)?P?u12n(X )u12?=1?X u12n,X+u1

24、2n?=X u12n?(2?)?n(X )N(0,1)?P?u12n(X )u12?=1?X u12n,X+u12n?=X u12n?(2?)?n(X )N(0,1)?P?u12n(X )u12?=1?X u12n,X+u12n?=X u12n?N(,0.92),?X1,X9?X=5.?95%?.?X u12n,X+u12n?n=9,u0.975=1.96,=0.9?X=5?5 0.99 1.96,5+0.99 1.96?=4.412,5.588?N(,0.92),?X1,X9?X=5.?95%?.?X u12n,X+u12n?n=9,u0.975=1.96,=0.9?X=5?5 0.99 1

25、.96,5+0.99 1.96?=4.412,5.588?(2?)?n(X )S t(n 1)?P?t12(n 1)n(X )S t12(n 1)?=1?X t12(n 1)Sn?(2?)?n(X )S t(n 1)?P?t12(n 1)n(X )S t12(n 1)?=1?X t12(n 1)Sn?(2?)?n(X )S t(n 1)?P?t12(n 1)n(X )S t12(n 1)?=1?X t12(n 1)Sn?12?(?)?4.684.854.324.854.615.025.204.604.584.724.384.70?95%?X Snt12(n 1)?X=4.70,S2=0.061

26、5.?t0.975(11)=2.2.?95%?4.7 0.061512 2.2=4.55,4.87?12?(?)?4.684.854.324.854.615.025.204.604.584.724.384.70?95%?X Snt12(n 1)?X=4.70,S2=0.0615.?t0.975(11)=2.2.?95%?4.7 0.061512 2.2=4.55,4.87?2?(?)?Pnk=1(Xk)22 2(n)?P?22(n)Pnk=1(Xk)22 212(n)?=1?Pnk=1(Xk)2212(n),Pnk=1(Xk)222(n)#?2?(?)?Pnk=1(Xk)22 2(n)?P?2

27、2(n)Pnk=1(Xk)22 212(n)?=1?Pnk=1(Xk)2212(n),Pnk=1(Xk)222(n)#?2?(?)?Pnk=1(Xk)22 2(n)?P?22(n)Pnk=1(Xk)22 212(n)?=1?Pnk=1(Xk)2212(n),Pnk=1(Xk)222(n)#?2?(?)?(n 1)S22 2(n 1)?P?22(n 1)(n 1)S22 212(n 1)?=1?(n 1)S2212(n 1),(n 1)S222(n 1)#?2?(?)?(n 1)S22 2(n 1)?P?22(n 1)(n 1)S22 212(n 1)?=1?(n 1)S2212(n 1),(n

28、 1)S222(n 1)#?2?(?)?(n 1)S22 2(n 1)?P?22(n 1)(n 1)S22 212(n 1)?=1?(n 1)S2212(n 1),(n 1)S222(n 1)#?2?pPnk=1(Xk)2q212(n),pPnk=1(Xk)2q22(n)?n 1Sq212(n 1),n 1Sq22(n 1)?2?pPnk=1(Xk)2q212(n),pPnk=1(Xk)2q22(n)?n 1Sq212(n 1),n 1Sq22(n 1)?4.?X N(1,21),Y N(2,22).?X1,X2,Xn?Y1,Y2,Ym?.?X,Y,S2X,S2Y.?1?(1)1 2;(2)2

29、1/22.?X N(1,21),Y N(2,22).?X1,X2,Xn?Y1,Y2,Ym?.?X,Y,S2X,S2Y.?1?(1)1 2;(2)21/22.?X N(1,21),Y N(2,22).?X1,X2,Xn?Y1,Y2,Ym?.?X,Y,S2X,S2Y.?1?(1)1 2;(2)21/22.?1 2?(21?22?)(1)21?22?X N?1,21n?,Y N?2,22m?(X Y)(1 2)q21n+22m N(0,1)?1 2?(X Y)u12r21n+22m?1 2?(21?22?)(1)21?22?X N?1,21n?,Y N?2,22m?(X Y)(1 2)q21n+22

30、m N(0,1)?1 2?(X Y)u12r21n+22m?1 2?(21?22?)(1)21?22?X N?1,21n?,Y N?2,22m?(X Y)(1 2)q21n+22m N(0,1)?1 2?(X Y)u12r21n+22m?1 2?(21?22?)(2)?21=22=2?X Y N?1 2,?1n+1m?2?S2W=(n 1)S2X+(m 1)S2Yn+m 2.?T=(X Y)(1 2)q1n+1mSW t(n+m 2).?(X Y)SWt12(n+m 2)r1n+1m.?1 2?(21?22?)(2)?21=22=2?X Y N?1 2,?1n+1m?2?S2W=(n 1)S2

31、X+(m 1)S2Yn+m 2.?T=(X Y)(1 2)q1n+1mSW t(n+m 2).?(X Y)SWt12(n+m 2)r1n+1m.?1 2?(21?22?)(2)?21=22=2?X Y N?1 2,?1n+1m?2?S2W=(n 1)S2X+(m 1)S2Yn+m 2.?T=(X Y)(1 2)q1n+1mSW t(n+m 2).?(X Y)SWt12(n+m 2)r1n+1m.?T t(n+m 2)?TT=U/pV/(n+m 2),?U=(X Y)(1 2)q1n+1mV=(n+m 2)S2W2=(n 1)S2X+(m 1)S2Y2.?S2X?S2Y?,?(n 1)S2X2

32、2(n 1),(m 1)S2Y2 2(m 1)?V 2(n+m 2)?T t(n+m 2).?T t(n+m 2)?TT=U/pV/(n+m 2),?U=(X Y)(1 2)q1n+1mV=(n+m 2)S2W2=(n 1)S2X+(m 1)S2Y2.?S2X?S2Y?,?(n 1)S2X2 2(n 1),(m 1)S2Y2 2(m 1)?V 2(n+m 2)?T t(n+m 2).?T t(n+m 2)?TT=U/pV/(n+m 2),?U=(X Y)(1 2)q1n+1mV=(n+m 2)S2W2=(n 1)S2X+(m 1)S2Y2.?S2X?S2Y?,?(n 1)S2X2 2(n 1)

33、,(m 1)S2Y2 2(m 1)?V 2(n+m 2)?T t(n+m 2).?1 2?(21?22?)?21?22?T=(X Y)(1 2)qS2Xn+S2Ym(3)?n?m?n 30?m 30?T?N(0,1).?(X Y)u12sS2Xn+S2Ym.?1 2?(21?22?)?21?22?T=(X Y)(1 2)qS2Xn+S2Ym(3)?n?m?n 30?m 30?T?N(0,1).?(X Y)u12sS2Xn+S2Ym.?1 2?(21?22?)(4)?T?t(v),?v=?S2Xn+S2Ym?2S4Xn2(n1)+S4Ym2(m1)?(X Y)t12(v)sS2Xn+S2Ym.?

34、1 2?(21?22?)(4)?T?t(v),?v=?S2Xn+S2Ym?2S4Xn2(n1)+S4Ym2(m1)?(X Y)t12(v)sS2Xn+S2Ym.?1 2?(21?22?)(5)?n=m?Zi=Xi Yi,?Zi?N(1 2,2)?2=21+22?.?1 2?Z1,Z2,Zn?Z,S2Z?Z t12(n 1)SZn.?1 2?(21?22?)(5)?n=m?Zi=Xi Yi,?Zi?N(1 2,2)?2=21+22?.?1 2?Z1,Z2,Zn?Z,S2Z?Z t12(n 1)SZn.?1 2?(21?22?)(5)?n=m?Zi=Xi Yi,?Zi?N(1 2,2)?2=21+

35、22?.?1 2?Z1,Z2,Zn?Z,S2Z?Z t12(n 1)SZn.?21/22?(1?2?)?T=S2X/21S2Y/22 F(n 1,m 1)?TT=A/(n1)B/(m1)?A=(n 1)S2X21 2(n 1)B=(m 1)S2Y22 2(m 1)?S2X?S2Y?,?A?B?T F(n 1,m 1)?21/22?(1?2?)?T=S2X/21S2Y/22 F(n 1,m 1)?TT=A/(n1)B/(m1)?A=(n 1)S2X21 2(n 1)B=(m 1)S2Y22 2(m 1)?S2X?S2Y?,?A?B?T F(n 1,m 1)?21/22?(1?2?)?T=S2X/

36、21S2Y/22 F(n 1,m 1)?TT=A/(n1)B/(m1)?A=(n 1)S2X21 2(n 1)B=(m 1)S2Y22 2(m 1)?S2X?S2Y?,?A?B?T F(n 1,m 1)?21/22?(1?2?)?P?F2(n 1,m 1)S2X/21S2Y/22 F12(n 1,m 1)?=1 P S2XS2Y1F12(n 1,m 1)2122S2XS2Y1F2(n 1,m 1)!=1?S2YS2X1F12(n 1,m 1),S2YS2X1F2(n 1,m 1)#?21/22?(1?2?)?P?F2(n 1,m 1)S2X/21S2Y/22 F12(n 1,m 1)?=1 P

37、 S2XS2Y1F12(n 1,m 1)2122S2XS2Y1F2(n 1,m 1)!=1?S2YS2X1F12(n 1,m 1),S2YS2X1F2(n 1,m 1)#?21/22?(1?2?)?5?6?5.065.085.035.005.07?4.985.034.974.995.024.95?21/22?.?S2XS2Y1F12(4,5),S2XS2Y1F2(4,5)#?S21=0.00037,S22=0.00092.?=0.05,?F0.025(4,5)=1F0.975(5,4)=19.36,F0.975(4,5)=7.39.?95%?0.0544,3.7657?21/22?(1?2?)

38、?5?6?5.065.085.035.005.07?4.985.034.974.995.024.95?21/22?.?S2XS2Y1F12(4,5),S2XS2Y1F2(4,5)#?S21=0.00037,S22=0.00092.?=0.05,?F0.025(4,5)=1F0.975(5,4)=19.36,F0.975(4,5)=7.39.?95%?0.0544,3.7657?21/22?(1?2?)?5?6?5.065.085.035.005.07?4.985.034.974.995.024.95?21/22?.?S2XS2Y1F12(4,5),S2XS2Y1F2(4,5)#?S21=0.0

39、0037,S22=0.00092.?=0.05,?F0.025(4,5)=1F0.975(5,4)=19.36,F0.975(4,5)=7.39.?95%?0.0544,3.7657?21/22?(1?2?)?5?6?5.065.085.035.005.07?4.985.034.974.995.024.95?21/22?.?S2XS2Y1F12(4,5),S2XS2Y1F2(4,5)#?S21=0.00037,S22=0.00092.?=0.05,?F0.025(4,5)=1F0.975(5,4)=19.36,F0.975(4,5)=7.39.?95%?0.0544,3.7657?21/22?

40、(1?2?)?5?6?5.065.085.035.005.07?4.985.034.974.995.024.95?21/22?.?S2XS2Y1F12(4,5),S2XS2Y1F2(4,5)#?S21=0.00037,S22=0.00092.?=0.05,?F0.025(4,5)=1F0.975(5,4)=19.36,F0.975(4,5)=7.39.?95%?0.0544,3.7657?21/22?(1?2?)?5?6?5.065.085.035.005.07?4.985.034.974.995.024.95?21/22?.?S2XS2Y1F12(4,5),S2XS2Y1F2(4,5)#?S

41、21=0.00037,S22=0.00092.?=0.05,?F0.025(4,5)=1F0.975(5,4)=19.36,F0.975(4,5)=7.39.?95%?0.0544,3.7657?5.4(?324?)?1?2?5?9?12?15?16?5.?L,U,?,?L,U,?,?L,U,?,?2?1?X t12(n 1)Sn,X+t12(n 1)Sn?L,UP?L?=P?n(X )S t12(n 1)?=1 2P?U?=P?n(X )S t12(n 1)?=1 2?.?2?1?X t12(n 1)Sn,X+t12(n 1)Sn?L,UP?L?=P?n(X )S t12(n 1)?=1 2

42、P?U?=P?n(X )S t12(n 1)?=1 2?.?2?1?X t12(n 1)Sn,X+t12(n 1)Sn?L,UP?L?=P?n(X )S t12(n 1)?=1 2P?U?=P?n(X )S t12(n 1)?=1 2?.?2?1?X t12(n 1)Sn,X+t12(n 1)Sn?L,UP?L?=P?n(X )S t12(n 1)?=1 2P?U?=P?n(X )S t12(n 1)?=1 2?.?(?1 )?L:P(L)=1 ,?/2?U:P(U)=1 ,?/2?(?1 )?L:P(L)=1 ,?/2?U:P(U)=1 ,?/2?(?1 )?L:P(L)=1 ,?/2?U:P(U)=1 ,?/2?(?1 )?L:P(L)=1 ,?/2?U:P(U)=1 ,?/2?(?1 )?L:P(L)=1 ,?/2?U:P(U)=1 ,?/2?X t12(n 1)Sn=4.55,4.87?=0.05,t0.975(11)=2.20.?X t1(n 1)Sn=4.58?=0.05,t0.95(11)=1.7959.?X t12(n 1)Sn=4.55,4.87?=0.05,t0.975(11)=2.20.?X t1(n 1)Sn=4.58?=0.05,t0.95(11)=1.7959.?5.5(?337?)?1?2?3?