In statistics what do these two phrases mean?
$$RV X : \Omega \rightarrow \mathbb{R}$$ and $$P(Z \Epsilon A)$$ I'll explain the parts I understand below...

Question

In statistics what do these two phrases mean?
$$RV X : \Omega \rightarrow \mathbb{R}$$ and $$P(Z \Epsilon A)$$ I'll explain the parts I understand below...

datanewb · Answer

X is a matrix, filled with real values... I don't know what the omega part means... is it clarifying that the basis of X is a subset of the real numbers?

For $$P(X\epsilon A)$$ it is the probability of X in A? I don't really know what that epsilon looking symbol means.

anonymous · Answer

The epsilon-looking symbol means "is an element of" - is set notation.

datanewb · Answer

Thank you! I will look up set notation!

Any thoughts on
$$RV X : \Omega \rightarrow \mathbb{R}$$?

anonymous · Answer

It's been a while since I've seen this notation, but I think the omega means "all" or "everything." The set that contains everything or everything in the set or similar.

datanewb · Answer

Okay, that makes sense in the context I'm reading.  Thank you again.

anonymous · Answer

No prob' I did a little more research and got two other definitions, so it depends on the context:
1. The last, the end, the ultimate limit of a set (though I think that is referring to lower-case omega if I remember right.
2. The sample space, or total set of all possible outcomes.

datanewb · Answer

Yes, in this case it was a sample space.