PDF-Three problems for the clairvoyant demon Georey Grimmett Abstract A number of tricky problems

Three of these proble ms are of Winkler type that is they are challenges for a clairvoya nt demon brPage 2br Edited by brPage 3br Three problems for the clairvoyant demon 11 Introduction Probability theory has emerged in recent decades as a crossr o. An ideal unbiased coin might not correctly model a real coin which could be biased slightly one way or another After all real life is rarely fair This possibility leads us to an interesting mathematical and computational question Is there some way w Figure 1 An example of an in64257nite discon tin uit y rom Figure 1 see that lim and lim Sa yin that limit is is i64256e from sa ying that the limit do sn exist the alues of are hanging in ery de64257nite as from either side Note that its not true t MON TO SAT MON TO SAT MON TO SAT MON TO SAT MON TO SAT MON TO SAT MON TO SAT MON TO SAT MON TO SAT MON TO SAT MON TO SAT MON TO SAT Dep . . . . . . . . 08.00 . . . . . . . . . . . . 13.15 . . . . . . 1. Chi-. Shung. Yip. Noah . Hershkowitz. JP Sheehan. Umair. . Suddiqui. University of Wisconsin – Madison. Greg Severn. University of San Diego. What is a Maxwell demon?. Maxwell imagined a being that could measure atomic speeds and let the fast ones pass and block the slow ones…... Mathematics in Today's . World. Last Time. We discussed the four rules that govern probabilities:. Probabilities are numbers between 0 and 1. The probability an event does . not. occur is 1 minus the probability that it . Suppose you have a coin with an unknown bias, . θ . ≡ P(head).. You flip the coin multiple times and observe the outcome.. From observations, you can infer the bias of the coin. Maximum Likelihood Estimate. Suppose you have a coin with an unknown bias, . θ . ≡ P(head).. You flip the coin multiple times and observe the outcome.. From observations, you can infer the bias of the coin. Maximum Likelihood Estimate. We . can’t . predict the result of a random event. . But that . doesn’t. mean we know . nothing . about random events. . For instance:. Equivalent outcomes . are . equally likely. Fair dice have 6 faces. Each number is . Clairvoyant is an adjective .. Foresee is a synonym for clairvoyant.. Clairvoyant is to be able to see the future.. . A clairvoyant person is a person who sees the future.. http://www.youtube.com/watch?v=3lcwfGayBco. Slide . 2. Probability - Terminology. Events are the . number. of possible outcome of a phenomenon such as the roll of a die or a fillip of a coin.. “trials” are a coin flip or die roll. Slide . February 16, 2015. In the last class. We started Ch. 4.4 in Mendenhall, Beaver, & Beaver. Today. Ch. 4.4-4.6 in Mendenhall, Beaver, & Beaver. Today. Sampling without Replacement. Permutations. Carl Sagan. 1934-1996. Astronomer. . cosmologist. . Astrophysicist. Cosmos: A Personal Voyage. . Pulitzer Prize. and the . Hugo Award. myelodysplastic syndrome. 25 chapters. . Nevada Math Project Day 1. WELCOME. MEET OUR PROJECT TEAM. D. A. V. E. L. E. N. N. Y. S. P. E. N. C. E. COIN TOSSES AT THE SUPERBOWL. Does the winner of the coin toss have an advantage at the . superbowl. Coin tossing sequences Martin Whitworth @ MB_Whitworth Toss a coin repeatedly until we get a particular sequence. e.g. HTT T T T H H T H T T 9 tosses How many tosses on average? Is it the same for all sequences?