[Math] disjoint subset of random variables

probability

Can someone explain me (possibly with examples) the meaning of the following statement: X and Y are two disjoint subsets of random variables? what this disjoint means here? I understand what disjoint means in terms of events, i.e if And B are two disjoint events then $A \cap B=\emptyset $, but what that means in the context of random variables? Thanks

Best Answer

For what it is worth, I see no reason why this could refer to the hypothesis that every random variable in $X$ should be independent of every random variable in $Y$, nor to the hypothesis that $X\cap Y$ should be empty. If I had to bet, I would bet that this simply refers to two collections of random variables.

Or, one is given previously some set $Z$ of random variables and the hypothesis is that $X\subseteq Z$, $Y\subseteq Z$, and $X\cap Y=\varnothing$.

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