2.2 Statistical Independence Two events A and B are statistically independent if the occurrence of one does not affect the occurrence of the other. This means P(A B)=P(A)and P(B A)=P(B). Now F(AIB)=P(An B) P(B) so if P(A B)=P(A)then P(AnB)=P(A)x P(B). We use this as our definition of statistical independence. Definition:Events A and B are statistically independent if P(A∩B)=P(A)P(B). For more than two events,we say: Definition:Events A1,A2....,An are mutually independent if P(A10A0...nAn)=P(A1)P(A2)...P(An),AND the same multiplication rule holds for every subcollection of the events too. Eg.events A,A2,A3.A are mutually independent if i)P(AnA）=P(A)P(A）for all i,j with i≠j: AND ii)P(AAjA)=P(A)P(Aj)P(Ax)for all i,j.k that are all different: AND iii)P()=P(A)P(A2)P(A3)P(A). Statistical independence for calculating the probability of an intersection We usually have two choices. 2.2 Statistical Independence Two events A and B are statistically independent if the occurrence of one does not affect the occurrence of the other. We use this as our definition of statistical independence. For more than two events, we say: Statistical independence for calculating the probability of an intersection We usually have two choices