Question: 2.4.3 Let X have a Poisson distribution with parameter > 0. Suppose itself is random, following an exponential density with parameter . (a)

2.4.3 Let X have a Poisson distribution with parameter  > 0. Suppose  itself is random, following an exponential density with parameter .

(a) What is the marginal distribution of X?

(b) Determine the conditional density for  given X D k.

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