Statistical Independence

Question 1

Definition 1:

Events A and B are independent iff

Answer 1

P(A | B) = P(A)

Question 2

Definition 2:

Events A and B are independent iff

Answer 2

P(A inter B) = P(A)P(B)

Question 3

Definition 3

Let A1,A2,…,Ak be events.

They are mutually independent iff

Answer 3

P(union Ai) = MULT P(Ai)

Question 4

Theorem:

Events A and B are disjoint.

A and B are independent iff

Answer 4

P(A) = 0

or

P(B) = 0

or both