  One of the most important discoveries in the observation of gamma-ray bursts
(GRBs) is that the total energy emitted by a GRB in gamma-rays has a very
narrow distribution around 10^51 erg, which has led people to claim that GRBs
are standard energy explosions. As people made the claim they have ignored the
selection biases which must be important since GRB observations are strongly
fluence or flux-limited. In this paper we show that, when the selection effects
are considered, the intrinsic distribution of the GRB energy can be very broad.
The number of faint GRBs has been significantly underestimated because of the
fluence or flux limit. The bright part of the distribution has been affected by
another important selection effect arising from the beaming of GRB jets, which
is instrument-independent and caused by the fact that brighter GRBs tend to
have smaller jet angles and hence smaller probabilities to be detected. Our
finding indicates that GRBs are not a standard energy reservoir, and challenges
the proposal that GRBs can be used as standard candles to probe cosmology.
