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cse63146
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Homework Statement
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.
Homework Equations
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]]]
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