Theory

Theory 1

Two events are independent when information about one of them does not change our probability estimate for the other.

Independence

Events and are independent when these (logically equivalent) equations hold:

Note that the last equation is symmetric in and :

• Check: and
• This symmetric version is the preferred definition of the concept of independence.

Multiple-independence

A collection of events is mutually independent when every subcollection satisfies:

A potentially weaker condition for a collection is called pairwise independence, which holds when all 2-member subcollections are independent:

One could also define -member independence, or -member independence. Plain ‘independence’ means any-member independence.