$Y\mid X\sim\mathrm{Poisson}(X)$ and $X\sim\mathrm{uniform}(a,b)$
Find the marginal distribution, mean and variance of $Y$.
Then, what happens if $X$ is normal?
$Y\mid X\sim\mathrm{Poisson}(X)$ and $X\sim\mathrm{uniform}(a,b)$
Find the marginal distribution, mean and variance of $Y$.
Then, what happens if $X$ is normal?