# Probability Generating Functions

• Aug 10th 2009, 04:33 AM
Zenter
Probability Generating Functions
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?
• Aug 10th 2009, 01:10 PM
mr fantastic
Quote:

Originally Posted by Zenter
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?

Are X and Y independent? Read this: Probability-generating function - Wikipedia, the free encyclopedia