Hello. How to find an explicit expression for the (1-) equitailed credible interval for . I know posterior which is beta. I am not sure what is explicit expression.

Here is the whole problem.

Quality control. Suppose that 10 products were inspected for the purpose of quality control and none of them were rejected. Answer the following. 1. Find the posterior mean of the probability of rejecting a product (). Assume a U (0, 1) prior distribution for . 2. Find an explicit expression for the (1 ) equitailed credible interval for . 3. Find an explicit expression for the (1 ) HPD credible interval for .