Let X,, X2, .. .be independent Cauchy random variables, each with PDF d f(x)= T(d² +x²)' Show that A, = (X, +X2++X,)/n has the same distribution as X.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 31E
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Let X1, X2, ... be independent Cauchy random variables, each
with PDF
d
f(x)=
TT(d² +x?)'
Show that A,= (X, +X2+•…+X„)/n has the same distribution as X,.
Transcribed Image Text:Let X1, X2, ... be independent Cauchy random variables, each with PDF d f(x)= TT(d² +x?)' Show that A,= (X, +X2+•…+X„)/n has the same distribution as X,.
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