  In time-domain measurements of a Poisson two-level system, the observed
transition rates are always smaller than those of the actual system, a general
consequence of finite measurement bandwidth in an experiment. This
underestimation of the rates is significant even when the measurement and
detection apparatus is ten times faster than the process under study. We derive
here a quantitative form for this correction using a straightforward
state-transition model that includes the detection apparatus, and provide a
method for determining a system's actual transition rates from
bandwidth-limited measurements. We support our results with computer
simulations and experimental data from time-domain measurements of
quasiparticle tunneling in a single-Cooper-pair transistor.
