The probability distribution of the beam-centre wanders and the probability distribution of the fluctuating average intensity measured by the point-aperture and caused by beam wander have been studied by using the probability theroy for laser beam propagation in a turbulent atmosphere. The resultS shown, the probability distribution of the two-dimension beam wandrs obeys Rician distribution, and the probability distribution of the average intensity fluctuations measured by the point-aperture satisfies Gamma distribution.