Independence of Events
Events are independent when , written . A collection of events is mutually independent when every finite subcollection satisfies .
Definition 2.8 (Independence of Events)
Let be a probability space. Let . We say that and are independent if
We write .
Let be a collection of events in . We say that are mutually independent if for any finite subset ,
Pairwise does not imply mutual
Pairwise independence does not imply mutual independence. Tossing a fair coin twice gives with for each outcome. The events
satisfy and , so they are pairwise independent. But , so they are not mutually independent.
Independence from complements
If , then :
Related
Stated in
- Definition 2.8 (Independence of Events)§2.3 Independence