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Homework Help: Moment Generating Function w/ Condtional Expectation

  1. Aug 15, 2009 #1
    1. The problem statement, all variables and given/known data

    Suppose [tex]\theta [/tex] ~ [tex]~ gamma(\alpha , \lambda) [/tex] where alpha is a positive integer. Conditional on [tex] \theta[/tex], X has a Poission distribution with mean [tex] \theta [/tex]. Find the unconditional distribution of X by finding it's MGT.

    2. Relevant equations

    3. The attempt at a solution

    So, this is what I interpreted the problem as:

    X = E[E[X|[tex]\theta[/tex]]] = E[[tex]\theta[/tex]] = [tex]\alpha \lambda[/tex]

    ext = e[tex]\alpha \lambda[/tex]t

    It's as far as I got. Any hints?

    or would I have to do this:

    ext = E[E[ext|[tex]\theta[/tex]]]
    Last edited: Aug 15, 2009
  2. jcsd
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