Considering a two-dimensional space $S$ of two random variables $X, Y$, is the following equality true or not for a p.m.f $f(x,y)$
$\sum_{(x,y) \in S} yf(x,y) = \mu_y$
I am having difficulty reconciling this with the definition that $\mu_y = \sum_{y \in S_y} yf_Y(y)$ where $f_Y(y) = \sum_{x \in S_X} f(x,y)$