Let be the proportion of students at a university who approve the government's policy on students' allowances. The students' newspaper is going to take a random sample of \(n=30\) students at a university and ask if they approve of the governments policy on student allowances.

(a) What is the distribution of \(y\), the number who answer yes ?

(b) Suppose 8 out of the 30 students answered yes. What is the frequentist estimate of .

(c) Find the posterior distribution \(g(y)\) if we use a uniform prior.

(d) What would be the Bayesian estimate of ?