Let $\displaystyle X_1,....,X_n$ be a random sample from a Bernoulli distribution, $\displaystyle X_i\sim BIN(1, \theta)$ and assume a uniform prior $\displaystyle \theta \sim UNIF(0,1)$. Derive a $\displaystyle 100(1-\alpha)$% Bayesian interval estimate of $\displaystyle \theta$.