  In this paper, we develop an approach for the exact determination of the
minimum sample size for estimating the parameter of an integer-valued random
variable, which is parameterized by its expectation. Under some continuity and
unimodal property assumptions, the exact computation is accomplished by
reducing infinite many evaluations of coverage probability to finite many
evaluations. Such a reduction is based on our discovery that the minimum of
coverage probability with respect to the parameter bounded in an interval is
attained at a discrete set of finite many values.
