(d) Consider three estimators

$$\hat{p}_U = \text{UMVUE found in (b)},$$

$\hat{p}_B$ = the posterior mean with constant risk found in (c-iii),

and

$$\hat{p}T = \begin{cases} \hat{p}U \text{ with probability } \frac{n}{n+1}, \\ 1/2 \text{ with probability } \frac{1}{n+1}. \end{cases}$$

(d-i) \((3\%)\) Find \(\sup{p\in (0,1)}R(p,\hat{p}U)\) \(\sup{p\in (0,1)}R(p,\hat{p}B)\) , and \(\sup{p\in (0,1)}R(p,\hat{p}T)\) for a fixed \(n\)