bursts contributed the most spectra at the highest temporal resolutions, while the dimmest bursts contributed few spectra, taken with relatively coarser binning. Clearly, as with the dimmer bursts from the actual observations, the longer temporal accumulations can average over significant spectral evolution in a single spectrum.

![The distribution of fitted [$E_{\rm peak}$]{} values for a simulation of a single, bright GRB pulse that has strong spectral evolution is shown as a histogram. Although the pulse is well sampled throughout its time history, the predominance of samples occurs at the peak of the pulse, heavily weighting the average spectrum with medium-energy [$E_{\rm peak}$]{} spectra. \[ephisto\]](sim40k_epeak_dist.pdf)

![The distribution of fitted [$E_{\rm peak}$]{} values is plotted as a histogram for fifty simulated single-pulse GRBs of ten different brightnesses and five different pulse asymmetries. Each simulated lightcurve has been binned to the same signal to noise ratio, resulting in different binning for each, while retaining similar statistics for the spectral fitting. The histogram represents the ensemble of all time-resolved spectra, similar to the BATSE or GBM Spectral Catalogs of Bright bursts, to be compared with Figure \[BATSE\_GBM\_Epeak\]. \[sim\_ep\_histo\]](sim_ep_histo.pdf)

The pulse histogram in Figure \[ephisto\] clearly has the largest contribution from the portion in the 