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Probability of coin and markov transition matrix

  1. Dec 19, 2006 #1
    1. Consider n flips of a fair coin. Calculate the probability:

    a. n/2 < -Total number of heads

    b. 5000 > total #heads

    c. n/2 < total #heads < 5n/8

    d. n < total #heads.

    WHERE n = 8992

    2. Consider the shopping problem
    Markov transition matrix

    .5 | .5
    -----------------
    .75 - k | .25 + k

    where k = 8992 divided by 20000..

    Start with initial v0 = (..5,.5) and describe the behavior of the
    system for many time steps.

    Does your result cycle, does one state become extinct, or does it
    approach a limit value?


    Any help will be nice.
     
  2. jcsd
  3. Dec 19, 2006 #2

    cristo

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    Staff Emeritus
    Science Advisor

    Is this a homework question? If so, please post your attempts at a solution, before we can help you.
     
  4. Dec 19, 2006 #3

    CRGreathouse

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    Science Advisor
    Homework Helper

    If you calculate the answer to #1a exactly, there are 2706 digits in the numerator and the same number in the denominator. :tongue2:
     
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