A mathematical model is introduced for spontaneous emission and shot-noise of a SASE FEL. A detailed study of statistical properties of the radiation from a SASE FEL operating has been performed with the help of a 1D time-dependent FEL code. The statistical properties of the radiation have been proved that the wider integrals of the instantaneous power follow a T distribution and the narrower integrals of that follow negative exponential distribution. The numerical and analytical results agree well.