Given $f(x,y) = \frac {xy^2}{13}$ over $(1,1), (1,2), (2,2)$, I am trying to find $f_X(x)$. By definition:
$f_X(x) = \sum_{y \in S_Y}f(x,y) = \frac {x}{13} + \frac {4x} {13} = \frac {5x}{13}$.
so that $f_X(1) = 5/13$ and $f_X(2) = 10/13 $. This is obviously wrong. Where am I going off?