A theory of noise in semiconductor devices is developed, expressing the intrinsic noise as the response of the electronic system to primary fluctuations of the electrons due to the statistical nature of the scattering events. The theory leads to a computational method complementing an existing technique for solving the Boltzmann equation for a device. The method is primarily aimed at noise in hot electron devices. It is applied to the transferred-electron amplifier, taking theoretical models of GaAs as definite examples and the predictions are compared with previous theory and experimental data.