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 ($\displaystyle \lambda$)

$\displaystyle \lambda$ : exponential ($\displaystyle \theta$)

And I simply need the marginal distribution of X and the conditional density for $\displaystyle \lambda$ 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?