Typically, lower confidence bounds (X) satisfying (3.21) also satisfy P{(X) < } 1 for

Typically, lower confidence bounds θ(X) satisfying (3.21) also satisfy Pθ{θ(X) < θ} ≥ 1 − α for all θ

so that θ is strictly greater than θ(X) with probability ≥ 1 − α. A similar issue of course also applies to upper confidence bounds. Investigate conditions where one can claim the endpoints are open endpoints. What happens in Example 3.5.2 for both the uniformly most accurate upper confidence bound, as well as the Clopper-Pearson solution?