Tangent of Uniform Distribution has Standard Cauchy Distribution/Examples/Radiation Particles

Example of Use of Tangent of Uniform Distribution has Standard Cauchy Distribution

Let particles be emitted from a source of radiation $S$ in a plane in random (equally likely) directions.

Let these particles travel in a straight line to a plane collector some distance from $A$.

Then the distribution of the points of impact of the particles on the collector has a standard Cauchy distribution.

Proof

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Sources

• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Cauchy distribution