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What is the distribution of the following event?

  1. Jun 2, 2012 #1
    1. The problem statement, all variables and given/known data

    See uploaded imagery.


    2. Relevant equations



    3. The attempt at a solution

    See uploaded imagery.


    I know that the distribution has something to do with the 1-dimensional Ising model being sampled via Gibbs sampler method, but that is all I know. Anyone have a hint/solution? Thanks.
     

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  3. Jun 2, 2012 #2

    Ray Vickson

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    For any [itex] a, b, c \in \{-1,1\}[/itex] we have
    [tex] P(x=a|y=b,z=c) = \frac{P(x=a \cap \{y=b,z=c\})}{P(y=b,z=c)} = \frac{P(x=a,y=b,z=c)}{P(y=b,z=c)},[/tex]
    where [itex]P(y=b,z=c) = \sum_{w=-1}^1 P(x=w,y=b,z=c).[/itex] This has nothing to do with Physics or the Ising model or anything else like that; it is just elementary probability.

    RGV
     
  4. Jun 2, 2012 #3
    Sorry, but I already got your answer (see imagery)... it's just that I do not know what distribution the conditional distribution follows...
     
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