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The amplitude distribution of apparent flux densities due to background or "confusion" sources observed by a pencil-beam telescope in a universe randomly populated by unresolved sources obeying a power-law number-flux-density relation is derived. It is shown that the detailed form of the distribution depends only on the number-count exponent and that the distribution width scales with beam shape and area in a way which also depends on this exponent, in disagreement with some earlier results. The confusion probability distributions are used to compute error distributions for confusion-limited flux-density measurements. A method for observing moving or variable sources weaker than the confusion limit is analyzed. Subject headings: radio radiation - radio sources
J. J. Condon (Fri,) studied this question.