第三次作业
page 100
5.由题可得a1 → 1,a2→ 2,a3→ 3
所以Fx(0)=0,Fx(1)=0.2,Fx(2)=0.5,Fx(3)=1,l(0)=0,U(0)=1
所以: a1 : l(1)=l(0)+( u(0) - l(0))FX(0)=0
U(1)=l(0)+( u(0)- l(0))FX(1)=0.2
a1a1: l(2)=l(1)+( u(1) - l(1))FX(0)=0
U(2)=l(1)+( u(1)- l(1))FX(1)=0.04
a1a1a3: l(3)=l(2)+( u(2) - l(2))FX(2)=0.02
U(3)=l(2)+( u(2)- l(2))FX(3)=0.04
a1a1a3a2: l(4)=l(3)+( u(3) - l(3))FX(1)=0.024
U(4)=l(3)+( u(3)- l(3))FX(2)=0.03
a1a1a3a2a3: l(5)=l(4)+( u(4) - l(4))FX(2)=0.027
U(5)=l(4)+( u(4)- l(4))FX(3)=0.03
a1a1a3a2a3a1: l(6)=l(5)+( u(5) - l(5))FX(0)=0.027
U(6)=l(5)+( u(5)- l(5))FX(1)=0.0276
所以a1a1a3a2a3a1的标签为 Tx(113231)=(U(6)+l(6))/2=0.0273
a1 → 1,a2→ 2,a3→ 3
所以 Fx(0)=0,Fx(1)=0.2,Fx(2)=0.5,Fx(3)=1,l(0)=0,U(0)=1
有公式t*=(tag-l(k-1))/(u(k-1) - l(k-1))
所以: t*=(0.63215699-0)/(1-0)=0.63215699
Fx(2)=0.5≤ t*≤Fx(3)=1
l(1)=l(0)+( u(0) - l(0))FX(2)=0.5
U(1)=l(0)+( u(0)- l(0))FX(3)=1 →a3
t*=(0.63215699-0.5)/(1-0.5)=0.26431398
Fx(1)=0.2≤ t*≤Fx(2)=0.5
l(2)=l(1)+( u(1) - l(1))FX(1)=0.6
U(2)=l(1)+( u(1)- l(1))FX(2)=0.75 →a2
t*=(0.63215699-0.6)/(0.75-0.6)=0.21437933333
Fx(1)=0.2≤ t*≤Fx(2)=0.5
l(3)=l(2)+( u(2) - l(2))FX(1)=0.63
U(3)=l(2)+( u(2)- l(2))FX(2)= 0.675 →a2
t*=(0.63215699-0.63)/(0.675-0.63)=0.047933111111
Fx(0)=0≤ t*≤Fx(1)=0.2
l(4)=l(3)+( u(3) - l(3))FX(0)=0.63
U(4)=l(3)+( u(3)- l(3))FX(1)=0.639 →a1
t*=(0.63215699-0.63)/(0.639-0.63)=0.23966555556
Fx(1)=0.2≤ t*≤Fx(2)=0.5
l(5)=l(4)+( u(4) - l(4))FX(1)=0.6318
U(5)=l(4)+( u(4)- l(4))FX(2)=0.6345 →a2
t*=(0.63215699-0.6318)/(0.6345-0.6318)=0.132218518519
Fx(0)=0≤ t*≤Fx(1)=0.2
l(6)=l(5)+( u(5) - l(5))FX(0)=0.6318
U(6)=l(5)+( u(5)- l(5))FX(1)=0.63234 →a1
t*=(0.63215699-0.6318)/(0.63234-0.6318)=0.661092592593
Fx(2)=0.5≤ t*≤Fx(3)=1
l(7)=l(6)+( u(6) - l(6))FX(2)=0.63207
U(7)=l(6)+( u(6)- l(6))FX(3)= 0.63234 →a3
t*=(0.63215699-0.63207)/(0.63234-0.63207)=0.3221851851852
Fx(1)=0.2≤ t*≤Fx(2)=0.5
l(8)=l(7)+( u(7) - l(7))FX(1)=0.632124
U(8)=l(7)+( u(7)- l(7))FX(2)= 0.632205 →a2
t*=(0.63215699-0.632124)/(0.632205-0.632124)=0.407283950617284
Fx(1)=0.2≤ t*≤Fx(2)=0.5
l(9)=l(8)+( u(8) - l(8))FX(1)=0.6321402
U(9)=l(8)+( u(8)- l(8))FX(2)=0.6321645 →a2
t*=(0.63215699-0.6321402)/(0.6321645-0.6321402)=0.690946502057
Fx(2)=0.5≤ t*≤Fx(3)=0.1 →a3
所以结果是a3a2a2a1a2a1a3a2a2a3