# Thread: mgf of a discrete random variable

1. ## mgf of a discrete random variable

A discrete random variable has pdf $p(y)=bk^y, y=0,1,2,...$
Find Y's mgf $m(t)$ generally.

I get a bit stuck on what to do..
I know that $m(t)=E(e^{ty})$
so $m(t)=\sum^{\inf}_{y=0}e^{ty}\cdot p(y)$which is equal to
$m(t)=\sum^{\inf}_{y=0}e^{ty}\cdot bk^y$ but I'm not too sure how to expand this out...

thanks for any help!

2. Hello,
Originally Posted by Robb
A discrete random variable has pdf $p(y)=bk^y, y=0,1,2,...$
Find Y's mgf $m(t)$ generally.

I get a bit stuck on what to do..
I know that $m(t)=E(e^{ty})$
so $m(t)=\sum^{\inf}_{y=0}e^{ty}\cdot p(y)$which is equal to
$m(t)=\sum^{\inf}_{y=0}e^{ty}\cdot bk^y$ but I'm not too sure how to expand this out...

thanks for any help!
You're almost there
Note that $e^{ty}=(e^t)^y$

Thus $e^{ty}\cdot bk^y$ can be written as $b(ke^t)^y$
And this is a geometric series

3. Thanks for that moo, i thought it was somethign similiar..
so $m(t)=\frac{b}{1-ke^t}$

the question also wants the mgf to be sketched when b=k=0.5 and to show the points t=0, t=0.2. I am a little bit confused, as to what the significance / point of drawing these points on the graph shows, and also the significance of the mgf graph? ie. i know about area under F(y) and f(y).. just wondering if there is a similiar significance for an mgf?