1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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.

    Attached Files:

    • hw.jpg
      File size:
      25.5 KB
  2. jcsd
  3. Jun 2, 2012 #2

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    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.

  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...
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook