Probability generating function for random variable

  • Thread starter tamintl
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  • #1
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Homework Statement


A random variable X has probability generating function gX(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:

gX(s) = E(sx) = Ʃ p(X=k)(sk)

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

Regards
Tam
 

Answers and Replies

  • #2
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What is [itex]g_X(0)[/itex]?? What is [itex]g^\prime_X(0)[/itex]?? (the derivative)
 
  • #3
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What is [itex]g_X(0)[/itex]?? What is [itex]g^\prime_X(0)[/itex]?? (the derivative)

[itex]g_X(0)[/itex] = 5-1= 1/5
[itex]g^\prime_X(0)[/itex]= 0
 
  • #4
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3,297
Yes, and what if you calculate the same thing using

[tex]g_X(s)=\sum P\{X=k\}s^k[/tex]

??
 
  • #5
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Yes, and what if you calculate the same thing using

[tex]g_X(s)=\sum P\{X=k\}s^k[/tex]

??

Not sure what u mean but [tex]g_X(0)=\sum P\{X=3\}0^3[/tex]=0 ???
Sorry
 
  • #6
22,129
3,297
Not sure what you mean but [tex]g_X(0)=\sum P\{X=3\}0^3[/tex]=0 ???
Sorry

OK, if you have the series

[tex]P\{X=0\}+P\{X=1\}s+P\{X=2\}s^2+...[/tex]

what happens if I put s=0??
 
  • #7
74
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OK, if you have the series

[tex]P\{X=0\}+P\{X=1\}s+P\{X=2\}s^2+...[/tex]

what happens if I put s=0??

You will get '0'
 
  • #9
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I'm not sure.. Sorry
 

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