Independence

• Events A and B are independent if .

• Example: A card is selected at random from an ordinary deck of cards.

  A = event that the card is an ace.
  B = event that the card is a diamond.

  

  

  

  

• Definition: Events A and B are independent if .

• Independence does NOT mean
  • That A and B have ``nothing to do with each other"

  • Or that A and B ``have nothing in common."

• Much better intuition on independence can be gained from the following (easily provable) fact:
  A and B are independent if and only if

  (equivalently, ). That is, if knowing B doesn't affect what you know about A, then A and B are independent.