  The Habitable Worlds Observatory (HWO) will seek to detect and characterize
potentially Earth-like planets around other stars. To ensure that the mission
achieves the Astro2020 Decadal's recommended goal of 25 exoEarth candidates
(EECs), we must take into account the probabilistic nature of exoplanet
detections and provide "science margin" to budget for astrophysical
uncertainties with a reasonable level of confidence. In this study, we explore
the probabilistic distributions of yields to be expected from a blind exoEarth
survey conducted by such a mission. We identify and estimate the impact of all
major known sources of astrophysical uncertainty on the exoEarth candidate
yield. As expected, eta_Earth uncertainties dominate the uncertainty in EEC
yield, but we show that sampling uncertainties inherent to a blind survey are
another important source of uncertainty that should be budgeted for during
mission design. We adopt the Large UV/Optical/IR Surveyor Design B (LUVOIR-B)
as a baseline and modify the telescope diameter to estimate the science margin
provided by a larger telescope. We then depart from the LUVOIR-B baseline
design and identify six possible design changes that, when compiled, provide
large gains in exoEarth candidate yield and more than an order of magnitude
reduction in exposure times for the highest priority targets. We conclude that
a combination of telescope diameter increase and design improvements could
provide robust exoplanet science margins for HWO.
