Rayleigh scattering in the transmission fiber will degrade the noise performance of fiber Raman amplifiers. In this paper, considering the impact of Rayleigh scattering in the transmission fiber, an analytical expression for the equivalent noise figure in a distributed fiber Raman amplifier is derived. This analytical expression is used to analyze the impact of Rayleigh scattering on the noise performance of a distributed fiber Raman amplifier and discuss the rule of pump power selection.