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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.

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.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter12: Probability
Section12.4: Discrete Random Variables; Applications To Decision Making
Problem 14E
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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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