  The analytical probability distribution of finite systems obeying
Bose-Einstein statistics in one, two, and three dimensions are investigated by
using a canonical ensemble approach. Starting from the canonical partition
function of the system, a unified approach is provided to study the probability
distribution of a condensate for various confinements and in different
dimensions. Based on the probability distribution function, it is
straightforward to obtain the mean ground state occupation number and particle
number fluctuations of the condensate. It is found that the particle number
fluctuations in a trapped Bose gas are strongly dependent on the type of
confining potential and on the dimensionality of the system.
