Do you have a typo?
It doesn't make sense that x is bounded above by 1
and x is larger than y
and yet you have 0<y<2
clearly y cannot pass 1.
Question: Find cdf (remember to consider all cases).
Shouldn't that be it? What's with these next two cases if x and y are never greater than 1 and 2 respectively?
Do I fundamentally misunderstand this problem?