  In this note we consider coverage of confidence intervals calculated with and
without systematic uncertainties. These calculations follow the prescription
originally proposed by Cousins & Highland but here extended to account for
different shapes, size and types of systematic uncertainties. Also two
different ordering schemes are considered: the Feldman & Cousins ordering and
its variant where conditioning on the background expectation is applied as
proposed by Roe & Woodroofe. Without uncertainties Feldman & Cousins method
over-covers as expected because of the discreteness of the Poisson
distribution. For Roe & Woodroofe's method we find under-coverage for low
signal expectations. When including uncertainties it becomes important to
define the ensemble for which the coverage is determined. We consider two
different ensembles, where in ensemble A all nuisance parameters are fixed and
in ensemble B the nuisance parameters are varied according to their
uncertainties. We also discuss the subtleties of the realization of the
ensemble with varying systematic uncertainties.
