[OJFord]

These things are marked by humans, and appealable (in the case of exams, if it's just homework who cares) - IME in the UK, if you write something like 'insufficient information in the question, given RVs are not independent' then you are not going to be marked down for it; if they find the question incorrect it'll likely be struck off entirely.

But more likely, everyone answers either wrong (not because they know better) or right, because they don't know to do anything but multiply them; at the stage this is a question they don't know there are dependent and independent RVs.

It's like if you draw something that looks near enough a square and show it to someone in primary school, asking for the angle in the corners. The correct answer is 90 degrees, it doesn't matter that it's not exactly drawn, that we didn't define a coordinate system or the units we wanted.

[qsort]

I don't doubt that what you say is true, but it strikes me as odd that they didn't sidestep the problem by picking an example where the variables are obviously uncorrelated.

It comes off as extremely sloppy: nobody expects kids in primary school to even understand what it means for variables to be independent, but certainly those writing the questions should know better!

[OJFord]

Just because they don't know better, or it's a mistake. I'm not suggesting they knowingly thought 'but that doesn't matter here we want a specific technically wrong answer'.

[jameshart]

I'm glad these unwritten rules are all clearly expressed so that all 3rd graders understand them.

Because if you didn't realize all the things you were allowed to assume at the level of math you are doing, it might be really stressful to be given problem for homework tat's unsolvable in general, but solvable if you make the correct set of assumptions, and think you are expected to produce a solution for it.

Especially that part about 'if it's homework, who cares'. I'm sure kids are very clear on that one.