a11=g11=0,911 | a12=a12=0,045 | a13=a13=3,369×10-4 | a14=a14=0,074 |
a21=b21= 0,125 | a22=g22=0,897 | a23=a23= 0,136 | a24=a24= 0,081 |
a31=b31=2,462×10-4 | a32=b32= 0,897 | a33=g33=0,928 | a34=a34=0,01 |
a41=b41=0,329 | a42=b42=0,19 | a43=b43=0.028 | a44=g44=0,933 |
Z (1.10.4).
G(Z)=0,2×0,911+0,4×0,897+0,3×0,928+0,1×0,933=0,913
-
, .
, ( ), ( ), , ( ).
() - () :
1. , . , .
2. . , .
, X ( ) - Y ( ) , : X ( Y).
, , .
.
m
x1 ;x2;...xm, p(x1);p(x2);...p(xm). .
x | x1 | x2 | ... | xm |
p | p(x1) | p(x2) | ... | p(xm) |
x1;x2;...xm - , , - (y1;y2;...ym) .
, , .
(1.11.1)
- , , Y . .
|
|
(1.11.2)
, . :
(1.11.3)
- i, , , . Y y1;y2;...ym. , xj , yi, j , aji, i.
, .
1.11.1
i\j | ... | m | |||
... | |||||
... | |||||
... | |||||
... | ... | ... | ... | aij | ... |
m | ... |
, .
, , , .
, gi .
, yj , i, .. , xi yj.
(1.11.4)
xi,.. yj , xi (p (yi/xi).
P(yi/xi) = (1.11.5)
.
1.11.2
i\j | y1 | y2 | y3 | ... | ym | |
x1 | 11 | 12 | 13 | ... | 1m | |
x2 | 21 | 22 | 23 | ... | 2m | |
x3 | 31 | 32 | 33 | ... | 3m | |
... | ... | ... | ... | ... | ... | ... |
xm | m1 | m2 | m3 | ... | mm |
p(x1); p(x2);... p(xm), ()
Pij=p(xy) = p(x)p(y/x) = p(y)p(x/y)
1.11.3
i\j | y1 | y2 | y3 | ... | ym | p(x) |
x1 | p11 | p12 | p13 | ... | p1m | p(x1) |
x2 | p21 | p22 | p23 | .. | p2m | p(x2) |
x3 | p31 | p32 | p33 | ... | p3m | p(x3) |
... | ... | ... | ... | ... | ... | ... |
xm | pm1 | pm2 | pm3 | ... | pmm | p(xm) |
p(y) | p(y1) | p(y2) | p(y3) | ... | p(ym) |
pij , y.
(1.11.6)
.
(1.11.7)
, .. ( ) ( ), , (1.11.3)
|
|
E(y/x) E(y/xi)- , xi.
(1.11.9)
. ( 1.11.2)
(1.11.10)
.
5.
x1,x2,x3,4.
(1)=0,2; p(x2)=0,4; p(x3)=0,3; (4)=0,1.
Z T. .
.1.11.1
.1.11.1 z.
, , .
a11=g11=0,911 | a12=a12=0,045 | a13=a13=3,369×10-4 | a14=a14=0,074 |
a21=b21= 0,125 | a22=g22=0,897 | a23=a23= 0,136 | a24=a24= 0,081 |
a31=b31=2,462×10-4 | a32=b32= 0,897 | a33=g33=0,928 | a34=a34=0,01 |
a41=b41=0,329 | a42=b42=0,19 | a43=b43=0.028 | a44=g44=0,933 |
, (1.11.1).
(1.11.1)
, , :
..
, (1.11.4)
(j/i).
i\ j | y1 | y2 | y3 | y4 |
X1 | 0,968 | 0,022 | 1,263×10-4 | 9,312×10-3 |
X2 | 0,042 | 0,877 | 0,068 | 0,013 |
X3 | 7,035×10-5 | 0,049 | 0,949 | 1,46×10-3 |
X4 | 0,072 | 0,084 | 9,429×10-3 | 0,834 |
, .. Y ( ) ().
Pij=() = ()(/)
():
i\j | y1 | y2 | y3 | y4 | p(x) |
X1 | 0,194 | 4,457×10-3 | 2,527×10-5 | 1,862×10-3 | 0,2 |
X2 | 0,017 | 0,351 | 0,027 | 5,384×10-3 | 0,4 |
X3 | 2,11×10-5 | 0,015 | 0,285 | 0,087 | 0,3 |
X4 | 0,218 | 8,43×10-3 | 9,429×10-4 | 0,083 | 0,1 |
p(y) | 0,218 | 0,378 | 0,313 | 0,091 | 1,0 |
.
,
, (1.11.9)
, , (1.11.10)
E(y/X) = 0,2×0,232+0,4×0,704+0,3×0,3+0,1×0,856 = 0,504
, , , : (1.11.3)
..
, z .
. n , , :
|
|
J=n
. , , .
- , , . - .