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UNR, MATH/STAT 352, Spring 2007

Probability and Statistics. MATH/STAT 352. Spring 2007. Lecture 11: Fair games, Bernoulli distribution, Binomial distribution. (slides only contain intro). UNR, MATH/STAT 352, Spring 2007. Fair games. UNR, MATH/STAT 352, Spring 2007. Tossing a symmetric coin. You are paying $1. Head.

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UNR, MATH/STAT 352, Spring 2007

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  1. Probability and Statistics MATH/STAT 352 Spring 2007 Lecture 11: Fair games, Bernoulli distribution, Binomial distribution (slides only contain intro) UNR, MATH/STAT 352, Spring 2007

  2. Fair games UNR, MATH/STAT 352, Spring 2007

  3. Tossing a symmetric coin You are paying $1 Head How much should you get to make the game fair? Tail UNR, MATH/STAT 352, Spring 2007

  4. Tossing a symmetric coin You are paying $1 Head Fair game You are getting $1 Tail UNR, MATH/STAT 352, Spring 2007

  5. Is a randomly chosen card the Queen of Spades? How much should you get to make the game fair? You pay $1 UNR, MATH/STAT 352, Spring 2007

  6. Is a randomly chosen card the Queen of Spades? P(Q♠) = 1/52 ≈ 0.02 UNR, MATH/STAT 352, Spring 2007

  7. Is a randomly chosen card the Queen of Spades? You get $51 Fair game You pay $1 UNR, MATH/STAT 352, Spring 2007

  8. What is a fair game? UNR, MATH/STAT 352, Spring 2007

  9. What is a fair game? In statistics, a fair game is a game with zero expected payoff. That is, let random variable X represent the amount that a player gets after one game; X > 0 means profit, X<0 means loss. Fair game means that UNR, MATH/STAT 352, Spring 2007

  10. What is a fair game? In statistics, a fair game is a game with zero expected payoff. In the coin tossing game, we have UNR, MATH/STAT 352, Spring 2007

  11. What is a fair game? In statistics, a fair game is a game with zero expected payoff. In the “Queen of spades” game, we have UNR, MATH/STAT 352, Spring 2007

  12. What is a fair game? In the “Deal or no Deal” game, we have UNR, MATH/STAT 352, Spring 2007

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