Expected Value

• The expected value is the long run average value of gain or loss from an experiment.
• Expected value is calculated in an experiment where there is a gain or loss.
• For an experiment
  • The outcomes are divided into a number of disjoint events which cover the entire outcome space.
  • Each event has an associated probability (P_i, for event i)
  • The sum of all probabilities must be 1.
  • And an associated gain/loss (A_i, for event i)
• E = A₁P₁ + A₂P₂ + ... + A_nP_n
• The fair price is the expected value + price to play.
  • This is the price to make the expected value 0 or a fair game.
• Try some exercises page 703 Make sure to do 23.