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One-sided confidence intervals are presented for the average of non-identicalBernoulli parameters. These confidence intervals are expressed as analyticalfunctions of the total number of Bernoulli games won, the number of rounds andthe confidence level. Tightness of these bounds in the sense of Buehler, i.e.as the strictest possible monotonic intervals, is demonstrated for allconfidence levels. A simple interval valid for all confidence levels is alsoprovided with a tightness guarantee. Finally, an application of the proposedconfidence intervals to sequential sampling is discussed.

Simple Buehler-optimal confidence intervals on the average success probability of independent Bernoulli trials