Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Moment generating function

  1. May 5, 2010 #1
    Is the following correct?

    [tex]M(t)=1+t\mu'_1+\frac{t^2}{2!}\mu'_2+\frac{t^3}{3!}\mu'_3+... =\sum_{n=0}^{\infty} \frac {E(Y^n)t^n}{n!}[/tex]

    Last edited: May 5, 2010
  2. jcsd
  3. May 5, 2010 #2
    I think that will only be true if your moment generating function is an exponential - in which case you are just doing a Taylor expansion. This is true for a Wiener process - but I don't think the relation you have holds in general.

  4. May 5, 2010 #3


    User Avatar
    Homework Helper

    m_Y(t) = E(e^{ty}) = \int e^{ty} \, dF(y) = \int \sum_{n=0}^\infty \frac{(ty)^n}{n!}\,dF(y) = \sum_{n=0}^\infty \left(\int \frac{(ty)^n}{n!} \, dF(y) \right)

    What do you get from working with the final form above?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook