Results 1 to 2 of 2

Math Help - Question about generating functions

  1. #1
    Member
    Joined
    Aug 2010
    Posts
    77

    Question about generating functions

    Find the generating function of the following mass function, and state where it converges.

    f(m)=\binom{n+m-1}{m}{p}^n{1-p}^m for m is greater or equal to 0

    I get:

    G_X(s)=\sum_{i=1}^{\infty} s^i \binom{n+m-1}{m}{p}^n{1-p}^m

    However I have no idea how to evaluate the sum
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Oct 2009
    Posts
    340

    Re: Question about generating functions

    Should be

    \begin{align*}G(s) &= \sum_{m = 1} ^ \infty s^m \binom{n + m - 1}{m}p^n (1 - p)^m \\ &= \sum_{m = 1} ^ \infty \binom{n + m - 1}{m} p^n [s (1 - p)]^m \end{align*}

    You can finish it I'm sure.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 0
    Last Post: April 19th 2011, 06:48 AM
  2. Replies: 0
    Last Post: April 15th 2011, 05:43 AM
  3. Combinatorics question - generating functions
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: November 4th 2009, 05:22 PM
  4. Generating Functions question
    Posted in the Discrete Math Forum
    Replies: 7
    Last Post: October 13th 2009, 02:43 PM
  5. Probability Generating Functions Question
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: February 15th 2009, 07:39 PM

Search Tags


/mathhelpforum @mathhelpforum