  The Clopper-Pearson confidence interval has ever been documented as an exact
approach in some statistics literature. More recently, such approach of
interval estimation has been introduced to probabilistic control theory and has
been referred as non-conservative in control community. In this note, we
clarify the fact that the so-called exact approach is actually conservative. In
particular, we derive analytic results demonstrating the extent of conservatism
in the context of probabilistic robustness analysis. This investigation
encourages seeking better methods of confidence interval construction for
robust control purpose.
