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Probability generating function for random variable

  1. Dec 10, 2011 #1
    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. jcsd
  3. Dec 10, 2011 #2

    micromass

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    What is [itex]g_X(0)[/itex]?? What is [itex]g^\prime_X(0)[/itex]?? (the derivative)
     
  4. Dec 10, 2011 #3
    [itex]g_X(0)[/itex] = 5-1= 1/5
    [itex]g^\prime_X(0)[/itex]= 0
     
  5. Dec 10, 2011 #4

    micromass

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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]

    ??
     
  6. Dec 10, 2011 #5
    Not sure what u mean but [tex]g_X(0)=\sum P\{X=3\}0^3[/tex]=0 ???
    Sorry
     
  7. Dec 10, 2011 #6

    micromass

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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??
     
  8. Dec 10, 2011 #7
    You will get '0'
     
  9. Dec 10, 2011 #8

    micromass

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    No, you won't. Check again.
     
  10. Dec 10, 2011 #9
    I'm not sure.. Sorry
     
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