怎样证A逆B逆独立

Question

如题所述

Answer 1

P(A的逆|B的逆）+P(A|B )=P(A的逆交B的逆）/P(B的逆）+P(AB )/P(B)
=[1-P(A并B）]/[1-P(B）]+P(AB )/P(B)=[1-P(A)-P(B)+P(AB)]/[1-P(B）]+P(AB )/P(B)
=1+[P(AB)-P(A)]/[1-P(B)]+P(AB )/P(B)=1
所以[P(AB)-P(A)]/[1-P(B)]=-P(AB )/P(B)
[P(AB)-P(A)]*P(B)=-[1-P(B)]*P(AB )
P(AB)*P(B)-P(A)P(B)=P(AB)*P(B)-P(AB)
所以P(A)P(B)=P(AB)
所以A与B相互独立