Question: Problem II.2. Suppose $X sim operatorname{EXP}(lambda) $ and $Y mid X sim operatorname{POISSON} (x) $. What is the joint distribution function? What is the marginal

 Problem II.2. Suppose $X \sim \operatorname{EXP}(\lambda) $ and $Y \mid X

Problem II.2. Suppose $X \sim \operatorname{EXP}(\lambda) $ and $Y \mid X \sim \operatorname{POISSON} (x) $. What is the joint distribution function? What is the marginal distributio n of $y$ ? Supposing that $Y=k$, what is the probability that $X=x$ ? SP.AS. 1588

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