Given the following probability mass function: $$ P_{xy}(x,y) = C\left(\frac{1}{2}\right)^x \cdot\left(\frac{1}{2}\right)^y $$ determine C.
$\textbf{Hint}$ : use the definition for a geometric series :
$$\sum_{n=0}^\infty r^n = \frac{1}{(1-r)}$$
edit: I'm not quite sure what to even do, I would normally integrate to find a constant? but I'm using geometric series now, and I don't really have any values for $x, y$ or $P_{xy}(x,y)$...
x and y can take any integer value equal or bigger then 0
Because $\sum\limits_{ \{x,y\} = 0}^\infty \left( {1 \over 2} \right)^x \left( {1 \over 2} \right)^y = {1 \over 1 - 1/2}{1 \over 1 - 1/2} = 4$, the normalization constant must be $C = 1/4$.