Suppose that the probability that a machine produces defective items is unknown and modelled as uniform on (0,1). Given the unknown probability, , of defective

Suppose that the probability that a machine produces defective items is unknown and modelled as uniform on (0,1). Given the unknown probability, Θ, of defective items, the results of a random sample may be modelled as Bernoulli trials with probability Θ. A random sample produces 1 out of 5 as defective. What is the posterior distribution for Θ given this data? What is the Bayes estimate? Give a 95% posterior probability interval for Θ.