  We present a prediction of the transiting exoplanet yield of the TESS primary
mission, in order to guide follow-up observations and science projects
utilizing TESS discoveries. Our new simulations differ from previous work by
using (1) an updated photometric noise model that accounts for the nominal
pointing jitter estimated through simulation prior to launch, (2) improved
stellar parameters based on Gaia mission Data Release 2, (3) improved
empirically-based simulation of multi-planet systems, (4) a realistic method of
selecting targets for 2-minute exposures, and (5) a more realistic geometric
distortion model to determine the sky region that falls on TESS CCDs. We also
present simulations of the planet yield for three suggested observing
strategies of the TESS extended mission. We report ~$10^4$ planets to be
discovered by the TESS primary mission, as well as an additional $\sim 2000$
planets for each year of the three extended mission scenarios we explored. We
predict that in the primary mission, TESS will discover about 3500 planets with
Neptune size and smaller, half of which will orbit stars with TESS magnitudes
brighter than 12. Specifically, we proposed a new extended mission scenario
that centers Camera 3 on the ecliptic pole (C3PO), which will yield more long
period planets as well as moderately irradiated planets that orbit F, G, and K
stars.
