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Formulas, tables, and graphs are given for the probability distribution of the instantaneous resultant amplitude of the sum of a constant vector and a Rayleigh-distributed vector. It is emphasized that two distributions are required to describe a Rayleigh-distributed vector: the distribution of its amplitude and the distribution of its phase. A summary is presented of physical conditions which must be satisfied for a given phenomenon to exhibit statistical properties of a Rayleigh-distributed vector. References are made to ways in which these distributions may be used to describe random variables occurring in ionospheric, tropospheric, and irregular terrain propagation problems. Finally, a discussion is given of amplitude and phase distributions of two other random vectors encountered in tropospheric propagation studies.