Binomial with unknown probability and sample size: some of the difficulties with setting prior distributions in multiparameter models can be illustrated with the simple binomial distribution. Consider data y1,...,yn modeled as independent Bin(N,) , with both N and unknown. Defining a convenient family of prior distributions on (N,) is difficult,partly because of the discreteness of N. Raftery (1988) considers a hierarchical approach based on assigning the parameter N a Poisson distribution with unknown mean . To define a prior distribution on (,N) , Raftery defines = and specifies a prior distribution on (,) . The prior distribution is specified in terms of rather than because 'it would seem easier to formulate prior information about , the unconditional expectation of the observations, than about , the mean of the unobserved quantity N .' a. A suggested noninformative prior distribution is p(,)1 . What is a motivation for this noninformative distribution? Is the distribution improper? Transform to determine p(N,)