Probability generating function for random variable

[tamintl]

Homework Statement

A random variable X has probability generating function g_X(s) = (5-4s²)^-1

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

Homework Equations

The Attempt at a Solution

Ehh don't really know where to go with one... I know:

g_X(s) = E(s^x) = Ʃ p(X=k)(s^k)

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

Regards
Tam

 

[micromass]

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

 

[tamintl]

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

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

 

[micromass]

Yes, and what if you calculate the same thing using

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

??

 

[tamintl]

Yes, and what if you calculate the same thing using

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

??

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

 

[micromass]

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

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??

 

[tamintl]

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??

You will get '0'

 

[micromass]

You will get '0'

No, you won't. Check again.

 

[tamintl]

I'm not sure.. Sorry