# Probability generating function for random variable

1. Dec 10, 2011

### tamintl

1. The problem statement, all variables and given/known data
A random variable X has probability generating function gX(s) = (5-4s2)-1

Calculate P(X=3) and P(X=4)

2. Relevant equations

3. The attempt at a solution
Ehh don't really know where to go with one... I know:

gX(s) = E(sx) = Ʃ p(X=k)(sk)

Nit sure how to proceed..
Any help would be great!!

Regards
Tam

2. Dec 10, 2011

### micromass

Staff Emeritus
What is $g_X(0)$?? What is $g^\prime_X(0)$?? (the derivative)

3. Dec 10, 2011

### tamintl

$g_X(0)$ = 5-1= 1/5
$g^\prime_X(0)$= 0

4. Dec 10, 2011

### micromass

Staff Emeritus
Yes, and what if you calculate the same thing using

$$g_X(s)=\sum P\{X=k\}s^k$$

??

5. Dec 10, 2011

### tamintl

Not sure what u mean but $$g_X(0)=\sum P\{X=3\}0^3$$=0 ???
Sorry

6. Dec 10, 2011

### micromass

Staff Emeritus
OK, if you have the series

$$P\{X=0\}+P\{X=1\}s+P\{X=2\}s^2+...$$

what happens if I put s=0??

7. Dec 10, 2011

### tamintl

You will get '0'

8. Dec 10, 2011

### micromass

Staff Emeritus
No, you won't. Check again.

9. Dec 10, 2011

### tamintl

I'm not sure.. Sorry