Let's say we have three random variables, $X$, $Y$ and $Z$, that depend on the roll of dice:
$$X= \left\{ \begin{array}{ll} 0 & \mbox{if the number on top is one.}\\ 1 & \mbox{otherwise.} \end{array} \right. $$ $$Y=\mbox{the number on top of the die.}$$ $$Z=XY$$
How do you interpret $Z$? It's the product of $X$ and $Y$, but are those measured in the same experiment or in different ones? i.e do they share the same die or use different dice?
The difference is significant, if they are dependent and share the same die, then $P(Z=1)=0$. If they use different dice, the probability changes: $P(Z=1)=P(X\neq1)P(Y=1)=\frac{5}{36}$
My question is: if you read the syntax above, would you interpret the variables to be dependent or independent? If you wanted to write it the other way around, what's the correct way to do it?