  Kepler has revolutionized the study of transiting planets with its
unprecedented photometric precision on more than 150,000 target stars. Most of
the transiting planet candidates detected by Kepler have been observed as
long-cadence targets with 30 minute integration times, and the upcoming
Transiting Exoplanet Survey Satellite (TESS) will record full frame images with
a similar integration time. Integrations of 30 minutes affect the transit
shape, particularly for small planets and in cases of low signal-to-noise.
Using the Fisher information matrix technique, we derive analytic
approximations for the variances and covariances on the transit parameters
obtained from fitting light curve photometry collected with a finite
integration time. We find that binning the light curve can significantly
increase the uncertainties and covariances on the inferred parameters when
comparing scenarios with constant total signal-to-noise (constant total
integration time in the absence of read noise). Uncertainties on the transit
ingress/egress time increase by a factor of 34 for Earth-size planets and 3.4
for Jupiter-size planets around Sun-like stars for integration times of 30
minutes compared to instantaneously-sampled light curves. Similarly,
uncertainties on the mid-transit time for Earth and Jupiter-size planets
increase by factors of 3.9 and 1.4. Uncertainties on the transit depth are
largely unaffected by finite integration times. While correlations among the
transit depth, ingress duration, and transit duration all increase in magnitude
with longer integration times, the mid-transit time remains uncorrelated with
the other parameters. We provide code in Python and Mathematica for predicting
the variances and covariances at www.its.caltech.edu/~eprice.
