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Discrete random variables and expected value

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Useful for: IB Math AA SL & HL IB Math AI SL & HL AP® Statistics

Learn it A probability distribution lists every value of X with its probability; the probabilities add to 1. The expected value E(X) = Σx·P(x) is the long-run average. A game is fair if the expected gain is 0.

Example: A game: win $10 with probability 0.1, $2 with 0.3, else $0. It costs $2 to play.

  1. E(win) = 10(0.1) + 2(0.3) = $1.60.
  2. Expected gain = 1.60 − 2 = −$0.40 per game: not fair.

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