In: Statistics and Probability
Consider a Bernoulli distribution f(x|θ) = θ^x (1 − θ)^(1−x) for x = 0 and x = 1. Let the prior distribution for θ be f(θ) = 6θ(1 − θ) for θ ∈ (0, 1).
(a) Find the posterior distribution for θ.
(b) Find the Bayes’ estimator for θ.