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

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Presentation transcript:

UNR, MATH/STAT 352, Spring 2007

Head Tail Tossing a symmetric coin You are paying $1 How much should you get to make the game fair?

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

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

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

UNR, MATH/STAT 352, Spring 2007

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 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 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 In the “Deal or no Deal” game, we have