Before I begin, I wanted to say I have gone through the following links which touch on this topic. 1. Link1 2. Link2 3. Link3 4. Link4 and what I understand is that joint density for dependent variables do not exist as it has zero Lebesgue measure. Is my understanding correct? If yes, can we find the expected value?
Let us consider 3 Random Variables $X$~$U(10,20)$, $Y$~$U(20,40)$ and $Z$~$U(20,70)$ which are related as $X+Y+Z=60$. Is there a way we can write the expectation and if we can, what does it intuitively mean?
Edit: Correcting mistake in initial question where $Z$~$U(40,60)$ which was wrong and as correctly pointed out by ClementC.