n 1, 2, , n, :
- iHj=Æ;
- , ..
H1È H2È .È Hn=Ω
1,n, 1 2, .
, . .
(1),, (Hn), , P(A|H1), P(A|H2), , P(A|Hn). ?
V . , 1- - 1, - 2. . , .
Ï :
1 , 2 . 1 2 . , (1)=(H2)=0.5. , , , P(A|H1)= 1. , , , P(A|H2)= 2. ()
. 1,, n P(H1),., P(Hn) P(A|H1), P(A|H2), , P(A|Hn). () :
() = P(H1) (A|H1)++ P(Hn) P(A|Hn),
.
.
=*Ω=*(1+2++Hn) = AH1 + AH2 + AHn .
()= (AH1)+ (AH2)++ (AHn)= *
(AH1) = P(H1) (A|H1)
(AH2) = P(H2) (A|H2)
..
(AHn) = P(Hn) (A|Hn)
* = P(H1) (A|H1) + + P(Hn) (A|Hn). <
V . . () - .
( .
()
).
H1, H2, H3 . P(H1)= P(H2)= P(H3)=1/3
(A|H1)= ½, (A|H2)= ¼, (A|H3)= 0
()= P(H1) (A|H1)+ P(H2) (A|H2)+ P(H3)(A|H3)=1/3*½+1/3*¼=¼. N
1,, n, . , (i) , .. . , ( ), .. P(H1| A) i- , .
|
|
. , () > 0 1,, n P(H1),., P(Hn) (A|H1), P(A|H2), , P(A|Hn). P(Hi| A) Hi
.
.
(AHi)= () P(Hi|A). P(Hi|A) = (AHi)/ () (*), () .
, (AHi)= P(Hi) (A|Hi). (*)
. <
P(Hi) (J ), P(Hi|A) (J ).
, . , ( ), , , .
()
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