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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?