  Observational biases distort our view of nature, such that the patterns we
see within a surveyed population of interest are often unrepresentative of the
truth we seek. Transiting planets currently represent the most informative data
set on the ensemble properties of exoplanets within 1 AU of their star.
However, the transit method is inherently biased due to both geometric and
detection-driven effects. In this work, we derive the overall observational
biases affecting the most basic transit parameters from first principles. By
assuming a trapezoidal transit and using conditional probability, we infer the
expected distribution of these terms both as a joint distribution and in a
marginalized form. These general analytic results provide a baseline against
which to compare trends predicted by mission-tailored injection/recovery
simulations and offer a simple way to correct for observational bias. Our
results explain why the observed population of transiting planets displays a
non-uniform impact parameter distribution, with a bias towards near-equatorial
geometries. We also find that the geometric bias towards observed planets
transiting near periastron is attenuated by the longer durations which occur
near apoastron. Finally, we predict that the observational bias with respect to
ratio-of-radii is super-quadratic, scaling as $(R_P/R_{\star})^{5/2}$, driven
by an enhanced geometric transit probability and modestly longer durations.
