Suppose the probability p of success on an experiment is given a prior with density $f_p(s)=2(1−s) \mathbb{1}_{[0,1]}(s)$. The experiment is independently conducted three times and is a success $N=2$ times.
What is the posterior mean of p?
Does anyone the steps to solving this problem?
$$\pi(s|\mathbf{x})\propto (1-s)s^2(1-s)=s^2(1-s)^2$$
That is a $Beta(3;3)$ thus the posterior mean is
$$\mathbb{E}[s|\mathbf{x}]=1/2$$