I am working on the 6.041 MIT Opencourseware course. Though, currently I am struggling with assignment 1b of the attached assignment (see pic).
As the joint pdf is linear (red circle), I do not see why the marginal PDF of Y can be quadratic (orange arrow). My feeling is that the provided solution mistakenly calculates the CDF.
What I did when trying to solve this; was to create a definite integral with bounds 1 and 2. In other words, replace the y (green arrow) with a 2. Though, as a result I would then have a new problem, as with this approach I would only have a constant (no variable) in my marginal PDF.
Do I have a mistake in my understanding? Thanks in advance!