We show analytically that the statistical error, α_τ, in estimating the optical depth, τ, due to microlensing is substantially higher than the naive Poisson estimate: σ_τ = (η/N)~(1/2)τ, where N is the number of detections and 1.65 ≤ η approx< 3. We construct a "microlensing map" using an observationally well-constrained barred bulge model and compare this with a map based on an axisymmetric bulge model. The result indicates a significant difference in the distribution of optical depths. If the optical depths are determined over a wide range of positions around the Galactic center, one could make a rudimentary determination of the geometry of the mass distribution of the Galactic bulge by observing ～700-800 events. About 1800 events are required to determine the relative contributions to lensing events by bulge and disk massive compact objects.
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