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$Y\mid X\sim\mathrm{Poisson}(X)$ and $X\sim\mathrm{uniform}(a,b)$

Find the marginal distribution, mean and variance of $Y$.

Then, what happens if $X$ is normal?

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    Hint for the "Then,..." part: In the definition of a Poisson random variable, are there any restrictions on the value of the parameter (usually denoted by $\lambda$)?2012-12-25

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