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Fair Games in Probability and Statistics

Dive into the concept of fair games with zero expected payoff in statistics. Learn about Bernoulli and Binomial distributions, fair coin toss games, and the Queen of Spades probability.

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Fair Games in Probability and Statistics

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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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