Finding the marginal distribution of a random variable w/ a random variable parameter

  • Thread starter ryzeg
  • Start date
  • #1
9
0
I am a little shaky on my probability, so bear with me if this is a dumb question...

Anyway, these two random variables are given:

X : Poisson ([tex]\lambda[/tex])
[tex]\lambda[/tex] : Exponential ([tex]\theta[/tex])

And I simply need the marginal distribution of X and the conditional density for [tex]\lambda[/tex] given a value for X

I have all the equations for dependent distributions, but do not know how to apply them to this ostensibly easy problem...

Any help?
 

Answers and Replies

  • #2
525
5


You'll need Bayes' rule for this. What results have you got so far?
 
  • #3
9
0


I was doing this, but I think it is wrong:

[tex]
f_X(x) = \int^{\lambda=\infty}_{\lambda=0} \frac{\lambda^{x}}{x!} e^{-\lambda} \times \theta e^{-\theta \lambda} d \lambda
[/tex]

Plugging this integral into Mathematica gives a really nasty output with a incomplete gamma function, and my TI-89T cannot evaluate it.
 
  • #4
9
0


I take that back; the integral is doable with a little manipulation. Damn machines...
 

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