  We study the impact of instrumental systematics on the variance, skewness,
and kurtosis of redshifted 21 cm intensity fluctuation observations from the
Epoch of Reionization. We simulate realistic 21 cm observations based on the
Murchison Widefield Array (MWA) Phase I reionization experiment, using the
array's point spread function (PSF) and antenna beam patterns, full-sky 21 cm
models, and the FHD imaging pipeline. We measure the observed redshift
evolution of pixel probability density functions (PDF) and one-point statistics
from the simulated maps, comparing them to the measurements derived from
simpler simulations that represent the instrument PSFs with Gaussian kernels.
We find that both methods yield statistics with similar trends with greater
than 80% correlation. We perform additional simulations based on the Hydrogen
Epoch of Reionization Array (HERA), using Gaussian kernels as the instrument
PSFs, and study the effect of frequency binning on the statistics. We find that
PSF smoothing and sampling variance from measuring the statistics over limited
field of view dilute intrinsic features and add fluctuations to the statistics
but reveal new detectable features. Observed kurtosis will increase when a few
extremely high or low temperature regions are present in the maps. Frequency
binning reduces the thermal uncertainty but can also blur regions along the
frequency dimension, resulting in kurtosis peaks that only appear in statistics
derived from maps of certain frequency bins. We further find that the kurtosis
peaks will reach their maxima when the angular resolution of the PSFs match the
size scale of the extreme regions that produce the peaks. The HERA array should
be capable of charting the evolution of the observed skewness and kurtosis of
the 21 cm fluctuations with high sensitivity while the MWA Phase I will likely
be capable of detecting the peak in variance.
