Two independent Poisson processes are each observed for a unit time. m and n incidents are observed respectively and the unknown rates (the Poisson means) are 0, and 0, respectively. If 0, and 0, have independent uniform prior distributions over the positive real line show that the posterior distribution of = 0/(0+0) has density (m+n+1)! m!n! (1-)". (*) Show that the conditional distribution of m, given m+n, depends only on . A statistician who wishes to make inferences about (but not about 0, and 0, separately) decides to use this last fact to avoid consideration of 0, and 0. Show that if he assumes y to have a uniform prior distribution in (0, 1) then he will obtain a posterior distribution identical to (*). Does this mean that m+n gives no information about ?