  It is pointed out that the quantum statistical phenomenon of Bosonic
stimulation, inherent to Bose statistics and the associated Bose-Einstein
correlation, can be effectively mapped on to the statistical problem of the
Polya urn scheme. Thus, we predict an irreproducibility for the limiting
non-degenerate values of the relative populations of two, or more equivalent
but separated condensates resulting from the fragmentation of a given source
condensate. Experiments are proposed that should verify this prediction $-$
using the dilute gas Bose-Einstein condensates, or a pulsed degenerate
multi-mode laser, where one would look for the run-to-run (or the
pulse-to-pulse) fluctuations of the relative populations.
