Let X be the number of successes from n independent Bernoulli trials with success probability p. 1. If we impose a prior distribution on p as the uniform distribution on (0, 1), find the Bayes estimator of p. 2. If the prior distribution on = p2 is uniform on (0, 1), what is the posterior mean of p. 3. The uniform prior is sometimes viewed as a prior that carries no prior information about the param