Results 1 to 2 of 2

Math Help - Moment Generating Function

  1. #1
    Newbie
    Joined
    Mar 2008
    Posts
    1

    Moment Generating Function

    Hi. I have a problem with this question:

    Let X be a discrete uniform random variable with pmf p_{X}(x)=\frac{1}{N}, for x=1,2,...,N. Find the mgf of X.

    What I did was:

    M_{X}(t)=E[e^{tx}]
    =\sum_{x=1}^N e^{tx}\frac{1}{N}
    =\frac{1}{N} \sum_{x=1}^N e^{tx}

    I don't know how to continue after that
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by Zayyym View Post
    Hi. I have a problem with this question:

    Let X be a discrete uniform random variable with pmf p_{X}(x)=\frac{1}{N}, for x=1,2,...,N. Find the mgf of X.

    What I did was:

    M_{X}(t)=E[e^{tx}]
    =\sum_{x=1}^N e^{tx}\frac{1}{N}
    =\frac{1}{N} \sum_{x=1}^N e^{tx}

    I don't know how to continue after that
    \sum_{x=1}^N e^{tx} = \sum_{x=1}^N (e^{t})^x

    is a geometric series. The first term is e^t and the ratio is e^t.

    If you scroll about two thirds of the way down this thread: Uniform Distribution -- from Wolfram MathWorld

    you'll find the answer you should get.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Moment Generating function
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: April 25th 2011, 02:49 PM
  2. Moment-Generating Function - Need help!!!
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: March 1st 2009, 06:40 PM
  3. moment-generating function
    Posted in the Advanced Statistics Forum
    Replies: 4
    Last Post: May 3rd 2008, 08:34 PM
  4. Moment-generating Function
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: March 28th 2008, 07:41 AM
  5. Moment generating function
    Posted in the Advanced Statistics Forum
    Replies: 4
    Last Post: February 2nd 2008, 02:27 AM

Search Tags


/mathhelpforum @mathhelpforum