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.
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