Probability theory MOC

Independence of events

Independent events are events which have no effect on each other's fruition — the knowledge that one occurred does not affect knowledge of whether the other occurred.

That is, the Conditional probability of one event given the occurance of the other is the same as the probability of the event. Note that pairwise independence does not necessarily imply independence. See also Independence of random variables.

Conditional independence

A related notion is conditional independence: Two events are conditionally independent given iff

Properties

1. Disjoint events can only be independent if one has zero probability
2. Two events can be
   • conditionally independent given but not independent
   • independent but not conditionally independent given
   • conditionally independent given but not given

#state/tidy | #SemBr | #lang/en