Let $\displaystyle \theta$ denote the proportion of registered voters in a large city who are in favour of certain proposition. Suppose that the value of $\displaystyle \theta$ is unknown and two statisticians A and B respectively use the following different prior distributions for $\displaystyle \theta$:

$\displaystyle h_{A}(\theta) = 2\theta, 0 < \theta < 1$
$\displaystyle h_{B}(\theta) = 4\theta^3, 0 < \theta < 1 $

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 $\displaystyle \theta$ and use the means of the posterior distributions to find point estimates for each statistician.