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# Ass7 - In a round of this game each player simultaneously...

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MATH 352 Assignment #7 Due: Tuesday December 4, 2007 1. Chapter 7 Problem 24. 2. Chapter 7 Theoretical Exercise 16. 3. Let F be a family of subsets of N = { 1 , 2 , . . . , n } that has the property that there are no sets A, B ∈ F which satisfy A B . Let σ = σ (1) σ (2) · · · σ ( n ) be a random permutation of the elements of N , and consider the random variable X = |{ i : { σ (1) , σ (2) , . . . , σ ( i ) } ∈ F}| . By considering the expected value of X , prove that |F| ≤ ( n n/ 2 ) . 4. Chapter 9 Theoretical Exercise 10. 5. Jason frequently babysits his younger cousin Julie, and on each occasion she wants to play games that Jason finds terribly boring. He always tries to win, since he figures that she’ll stop making him play games if she always loses. Lately Julie wants to play “Rock, Paper, Scissors”.
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Unformatted text preview: In a round of this game, each player simultaneously makes a hand motion representing one of rock, paper, or scissors. If the two players do not pick the same item, a winner is determined by the rule: rock smashes scissors, paper covers rock, scissors cut paper. After playing for a while, Jason realizes that whenever Julie wins, she always picks a diﬀerent action on the next turn, and when she loses, she either picks the same item again or she picks the item she lost against. When they pick the same item, her next choice is random. Using his observations, Jason can play with a strategy rather than just by chosing randomly. If he does this, what proportion of games will Julie win?...
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