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The statistical properties of the EEG and the MEG can be described mathematically as the result of randomly distributed dipoles representing the interactions of cortical neurons. If the dipoles are in a spherical volume conductor and have no preference for any direction, the variance of a differentially measured EEG signal is only a function of the electrode distance. The theoretically derived variance function is compared with EEG and MEG measurements. It is shown that a dipole with a fixed position and a randomly fluctuating amplitude is an adequate model for the alpha -rhythm. An expression for the covariance between the magnetic field and a differentially measured EEG signal is derived. This covariance is considered as a function of the magnetometer position. The theory can be used to obtain a (spatial) covariance matrix of the background noise, which occurs in evoked potential measurements. Such a covariance matrix can be used to obtain a maximum likelihood estimator (MLE) of the dipole parameters in evoked potential studies.