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This is a tutorial paper, written by the Subcommittee on Noise, IRE 7.9, to provide the theoretical background for some of the IRE Standards on Methods of Measuring Noise in Electron Tubes. The general-circuit-parameter representation of a linear two-port with internal sources and the Fourier representations of stationary noise sources are reviewed. The relationship between spectral densities and mean-square fluctuations is given and the noise factor of the linear twoport is expressed in terms of the mean-square fluctuations of the source current and the internal noise sources. The noise current is then split into two components, one perfectly correlated and one uncorrelated with the noise voltage. Expressed in terms of the noise voltage and these components of the noise current, the noise factor is then shown to be a function of four parameters which are independent of the circuit external to the twoport.