Conditional Independence

Definition:

• $P(A\cap B)=P(A|B)P(B)$
• Event A and B are conditional independent given an event C:
  • $P(A,B|C)=P(A|C).P(B|C)$`
• $A\perp \perp B|C$ : Event A is conditional indepedent to B given C
  • if and only if: $P(A,B|C)=P(A|C).P(B|C)$
  • ie if and only if: $P(A|B,C)=P(A|C)$