Expected Value

• The expected value of an experiment is the expected profit/loss when conducting an experiment over the long term.
• To compute expected value
  • You need a set of events E_i such that ∪E_i = U
  • P(E_i) = P_i
  • The gain or loss for each E_i is A_i
  • Expected Value = ΠP_iE_i
  • Expected value = P₁A₁ × P₂A₂ ... × P_nA_n
• The fair price is the amount to be paid that will result in an expected value of 0.
  • IE, there is no long term profit or loss from playing the game.
  • Fair Price = expected value + cost to play
• Try some problems page 658
• Make sure to do 22-24