What is the distribution of the following event?

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.

Ray Vickson

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

number0

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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Ray Vickson Recognitions: Homework Help	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

number0	Sorry, but I already got your answer (see imagery)... it's just that I do not know what distribution the conditional distribution follows...