Results 1 to 2 of 2

Math Help - Proof of MGF Theorm

  1. #1
    Newbie
    Joined
    Oct 2009
    Posts
    20

    Proof of MGF Theorm

    I'm stuck on trying to prove three theorms in the moment generating function below. The image is a screen shot of what I've done (I believe the first part I've proven, but the second and third theorms I don't really understand how to prove after it out to the points in the screenshot. Can someone show me how to prove them? Thanks!

    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Oct 2009
    Posts
    340
    Part 2: Define Y = Xb. M_{Xb} (t) = M_Y (t) = E[e^{Yt}] = E[e^{Xbt}] = E[e^{X(bt)}] = M_X (bt). Remember that when we write down M_X (t), t is just some argument. If we wanted to evaluate M_X (bt), we would just use the definition of the MGF to end up with E[e^{X(bt)}].

    Part 3: Do the same thing basically, remembering that, with respect to the expectation operator, everything other than X is a constant, and can be moved in an out with the usual rules. You should also use this method to redo part 1, since your method of just replacing X with whatever function of X you want hasn't exactly been justified.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Fundamental Theorm
    Posted in the Calculus Forum
    Replies: 3
    Last Post: April 20th 2010, 06:19 PM
  2. recurrence Master Theorm proof
    Posted in the Advanced Applied Math Forum
    Replies: 2
    Last Post: October 30th 2009, 11:43 AM
  3. Proof for Part 2 of the fundamental theorm
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: October 30th 2009, 05:18 AM
  4. Residue Theorm - Q1
    Posted in the Differential Geometry Forum
    Replies: 6
    Last Post: October 3rd 2009, 08:35 AM
  5. Remainder Theorm
    Posted in the Algebra Forum
    Replies: 1
    Last Post: May 17th 2008, 11:49 AM

Search Tags


/mathhelpforum @mathhelpforum