# What is the distribution of the following event?

1. Jun 2, 2012

### number0

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.

File size:
25.5 KB
Views:
62
2. Jun 2, 2012

### Ray Vickson

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

RGV

3. Jun 2, 2012

### number0

Sorry, but I already got your answer (see imagery)... it's just that I do not know what distribution the conditional distribution follows...

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook