# #StackBounty: #probability #inference #terminology #causality #causal-diagram Determining direct cause with some "realization&quot…

### Bounty: 100

I’m bouncing around "Causality" by Judea Pearl.

On page 222 it offers this definition of a direct cause:

"$$X$$ is a direct cause of $$Y$$" if there exist two values $$x$$ and $$x’$$ of $$X$$ and a value $$u$$ of $$U$$ such that $$Y_{xr}(u) not= Y_{x’r}(u)$$ where $$r$$ is some realization of $$V setminus {X, Y}$$.

My questions are:

1. What is a "realization", is it the same as Wikipedia’s Realization (probability) definition?
2. What does the $$setminus$$ symbol mean in the context of the two functions $$X$$ and $$Y$$? Can you give me an example?
3. Finally, how do I use this definition in practice?

Let’s say I have two structural causal models:

1. $$X rightarrow Y$$
2. $$X rightarrow Q rightarrow Y$$

How does this definition of direct cause allow me to discover that $$X$$ is a direct cause in the first case, and $$X$$ is not a direct cause in the second case?

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