1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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
    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
    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
    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
    No, you won't. Check again.
     
  10. Dec 10, 2011 #9
    I'm not sure.. Sorry
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook




Loading...