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Probability, Expected Value, Variability

measuring risk - must know all possible outcomes, probability of each outcome 

  • sum of probabilities = 1
  • objective interpretation - based on past events/experiments
  • subjective interpretation - based on educated guess about future
  • expected value, variability >> characterize payoff/risk
  • expected income (value) = sum of product of probability and payoffs
    • probability of each case can change based on personal skills/tendencies
    • expected values same >> variability not always the same
    • E(X) = probability1(X1) + probability2(X2) + ...
  • deviations - difference between expected and actual payoff
    • based on deviations from the mean
    • standard deviation - measures risk, equal to square root of average of squares of deviations
    • Ö(probability1(deviation1)2 + probability2(deviation2)2)
    • people generally want less risk
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