Results 1 to 6 of 6

Math Help - Poisson PGF

  1. #1
    Newbie
    Joined
    Dec 2009
    Posts
    5

    Poisson PGF

    Im not sure where to start with this. Im thinking i may have to start off by intergrating the poisson distribution over 0 to infinity?

    If X ~ P(mu), show that its PGF (Probability Generating Function) is given by:

    Gx(s) = e^{mu(s-1)}

    Sorry i have used the word "mu" instead of the symbol, i kept encountering LaTex problems
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Dec 2009
    From
    Lima OH
    Posts
    11
    Are you starting with the Poisson distribution and replacing
    lamda with mu since it can shown using infinite series that the population mean of the Poisson distribution is mu=lamda? I think you can integrate that to get the correct answer, but I haven't had time to try it yet. Let me know what you come up with.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member chella182's Avatar
    Joined
    Jan 2008
    Posts
    267
    I'm in the same class as whoever posted this, and \mu is just the parameter of the distribution... nothing to do with the mean. I also have no idea how to do about proving it, though.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Dec 2009
    Posts
    6
    The expected value of your poisson is \mu, which is probably why your professor uses it there.

    anyways, expand out your p.g.f., rearrange it so that within your infinite sum, you set up a new poisson with the parameter as s\mu, and on the outside, you'll have the e^(mu(s-1)) you're looking for

    Quote Originally Posted by chella182 View Post
    I'm in the same class as whoever posted this, and \mu is just the parameter of the distribution... nothing to do with the mean. I also have no idea how to do about proving it, though.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Senior Member chella182's Avatar
    Joined
    Jan 2008
    Posts
    267
    I know that's how you do it, it's just not coming out right, hence how I'm stuck.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by chella182 View Post
    I know that's how you do it, it's just not coming out right, hence how I'm stuck.
    The problem is trivial if you realise (and you should at this level) that \sum_{x=0}^{+\infty} \frac{(s \lambda)^x}{x!} = e^{s \lambda} (that is, recognise the well known Maclaurin series for e^{t}).

    Please show all details of your calculations.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Poisson Square Wave (PSW) and Filtered Poisson Process (FP)
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: April 5th 2010, 12:56 PM
  2. poisson
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: December 8th 2009, 02:21 AM
  3. Poisson Q help plz
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: May 4th 2009, 07:58 PM
  4. Poisson
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: April 7th 2009, 05:41 PM
  5. poisson iid
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: October 4th 2008, 09:43 PM

Search Tags


/mathhelpforum @mathhelpforum