Suppose the following joint pdf:
$f_{X,Y}(x,y) = \frac{3}{2}x$ if $1\leq x \leq 2$ and $0 \leq y \leq x$.
Note that $f_{X,Y}(x,y) = 0$ otherwise.
I am told to calculate the marginal pdf for $Y$, that is, $f_Y(y)$. In this case, I have to fix $y$ and integrate over $x$.
I calculated $f_Y(y)$ as $\int_{y}^{2} \frac{3}{2}x~ dx$. But in fact it should be solved as $\int_{1}^{y} \frac{3}{2}x~ dx$. Can someone explain me why the set of interest is $\int_{1}^{y}$ and not $\int_{y}^{2}$? And can you help me first drawing the region of interest?
Any help will be very appreciated.