Question: 4.3. Let X have a Poisson distribution with parameter A > 0. Suppose A itself is random, following an exponential density with parameter 0. (a)

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

(a) What is the marginal distribution of X?

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

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