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Math Help - Moment generating function

  1. #1
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    Moment generating function

    Consider a hierarchical model that defines the joint distribution of (X,Z). Let
    X|Z=z ~ N(0,z^2) where Z ~ N(0,1). Determine the moment generating function of X.

    My solution so far is attached. Am I going in the right direction? If so, how do I solve the integral for the marginal PDF of X? Or am I doing completely useless stuff?

    Thanks
    Attached Files Attached Files
    Last edited by mr fantastic; April 27th 2009 at 03:22 AM.
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  2. #2
    MHF Contributor matheagle's Avatar
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    1 Your attachment has errors in it
    2 I also started working on this IGNORING the MGF comment
    3 THEN I realized that z is your standard deviation, hence it cannot be a N(0,1) rv, try a chi-square maybe. Or U(0,1)?
    Last edited by matheagle; April 26th 2009 at 10:24 PM.
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