  We calculate the statistical distribution of observed afterglow flux, in some
fixed observed frequency band, and at some fixed observer time after the
explosion ($t_{obs}$) in two models - one where the explosion takes place in a
uniform density medium and the other where the surrounding medium has a
power-law stratification such as is expected for a stellar wind. For photon
energies greater than about 500 electron-volt and $t_{obs}\gta 10^3$ sec the
afterglow flux distribution functions for the uniform ISM and the wind models
are nearly identical. We compare the width of the theoretical distribution with
the observed x-ray afterglow flux and find that the FWHM of the distribution
for energy in explosion and the fractional energy in electrons ($\epsilon_e$)
are each less than about one order of magnitude and the FWHM for the electron
energy index is 0.6 or less.
