I have some problems in figuring out how to address the following problem and some help would be welcomed.
Exercise
Consider a Continuous Uniform Distribution over the $ (a,b)$ interval where $a< b$ are both unknown parameters.
a) Find a joint prior distribution for the vector of parameters $(a,b)$ such that it is conjugate family for the Uniform$(a,b)$ distribution.
b) Based on a) find the prior marginal distribution for each parameter.