Given:

$\displaystyle G_{X}(z) = \frac{1}{2}(1+z)$

and

$\displaystyle

G_{Y}(z) = \frac{5}{7-2z}$

What is the pgf of the random variable $\displaystyle V = X + Y$?

I've figured out the pmfs as:

$\displaystyle p_{x} = \frac{1}{2}(1)^x$

$\displaystyle p_{y} = \frac{5}{7}(\frac{2}{7})^y$

Firstly, are the pmfs correct? I feel like I've missed something really obvious but I can't tell...

Secondly, how would I find the pgf of V, as asked above?