+ Reply to Thread
Results 1 to 2 of 2

Thread: Reversing the moment generating function

  1. #1
    Points: 1,535, Level: 22
    Level completed: 35%, Points required for next Level: 65

    Posts
    18
    Thanks
    3
    Thanked 0 Times in 0 Posts

    Reversing the moment generating function




    So this is my moment generating function

    \frac{e^{-2t}+e^{-t}+e^{t}+e^{2t}}{4}

    Now i need to find the PDF or CDF

    So i think the moment genereting function needs to be divided by e^{tx}

    But how do i do this in an algabraic way
    This is what i got so far

    \frac{e^{-2t}*e^{tx}+e^{-t}*e^{tx}+e^{t}*e^{tx}+e^{2t}*e^{tx}}{4}

    And now i'm stuck

  2. #2
    TS Contributor
    Points: 22,410, Level: 93
    Level completed: 6%, Points required for next Level: 940

    Posts
    3,020
    Thanks
    12
    Thanked 565 Times in 537 Posts

    Re: Reversing the moment generating function


    Note that the mgf of a random variable X is defined by

    M_X(t) = E[e^{tX}]

    and mathematically speaking it is a Laplace transform of the corresponding pmf/pdf. Now you are given the mgf, and want to find the corresponding pmf/pdf, so generally speaking you would like to do an inverse-Laplace transform. There are table for this for many common functional form.

    However, your mgf is easy enough to recognize. Think about how do you calculate the mgf for a discrete distribution, say a Binomial distribution. Then you can match the corresponding probabilities and support points. Also note that the Laplace transform is unique so you will have a unique solution.

+ Reply to Thread

           




Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts






Advertise on Talk Stats