Suppose that $X_1,\ldots,X_n$ is a random sample from $U(θ,θ+1),$ and further assume $θ$ has a prior distribution as the discrete uniform distribution on the integers $1,2,\ldots,n$ where $n$ is known. Obtain the posterior distribution of $θ.$
The problem is that as the joint distribution has an indicator function, then I don't know how to integrate the product of this times $1/n$ (the prior distribution).
Any one could help me with that?
Thank you in advance.