Let denote the proportion of registered voters in a large city who are in favour of certain proposition. Suppose that the value of is unknown and two statisticians A and B respectively use the following different prior distributions for :
In a random sample of 1000 registered voters from this city it was found that 710 are in favour of the proposition.
Find the posterior distribution that each statistician assignments to and use the means of the posterior distributions to find point estimates for each statistician.