I am given that $N \sim \operatorname{Poisson}(1)$. Conditioned on $N = n$, let $X$ have uniform distribution over integer $n = 0,1,\ldots,n+1$.[sic] What is the marginal distribution of $X$?
I used the law of total probabilities but the result doesn't come up to a specific distribution. Is it possible it just have a probability mass function that doesn't match up to any common distributions?
Thanks!