lMIT6_042JS10_lec35

# lMIT6_042JS10_lec35 - Guess the Bigger Number Mathematics...

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1 Albert R Meyer, May 3, 2010 lec 13M.1 Mathematics for Computer Science MIT 6.042J/18.062J Introduction to Random Variables Albert R Meyer, May 3, 2010 lec 13M.2 Guess the Bigger Number Team 1: ! Write different integers between 0 and 7 on two pieces of paper ! Show to Team 2 face down Team 2: ! Expose one paper and look at number ! Either stick or switch to other number Team 2 wins if gets larger number Albert R Meyer, May 3, 2010 lec 13M.4 Strategy for Team 2 ! pick a paper to expose giving each paper equal probability. ! if exposed number is “small” then switch, otherwise stick. That is switch if ! threshold Z where Z is a random integer, 0 ! Z ! 6. Albert R Meyer, May 3, 2010 lec 13M.5 Analysis of Team 2 Strategy Case M: low ! Z < high Team 2 wins in this case, so Pr{Team 2 wins | M} = 1 and Pr{M} = " Albert R Meyer, May 3, 2010 lec 13M.6 Analysis of Team 2 Strategy Case H: high ! Z Team 2 will switch, so wins iff low card gets exposed Pr{Team 2 wins | H} = Albert R Meyer, May 3, 2010 lec 13M.7 Case L: Z < low Team 2 will stick, so wins iff high card gets exposed Pr{Team 2 wins | L} = Analysis of Team 2 Strategy

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## lMIT6_042JS10_lec35 - Guess the Bigger Number Mathematics...

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