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Sample Means of Independent Standard Cauchy Random Variables Are Standard Cauchy: A New Approach
Michael P. Cohen
The American Mathematical Monthly
Vol. 119, No. 3 (March 2012), pp. 240-244
Published by: Mathematical Association of America
Stable URL: http://www.jstor.org/stable/10.4169/amer.math.monthly.119.03.240
Page Count: 5
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Abstract A remarkable property of the Cauchy distribution is that the sample mean of standard Cauchy random variables itself has a standard Cauchy distribution. This result can be shown using characteristic functions, convolution integrals, or multidimensional change of variables (Jacobians). A new method of proof based on the periodicity properties of the tangent function is presented.
Copyright the Mathematical Association of America 2012