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The Cauchy distribution with scaling parameter 7, C(0, 7), has density 1 TT1+ (z/7)2" 1 f(z; T) = ZER. and characteristic function (r) = eTal (you can take this for granted). (1) (optional). Show that if X ~ C(0, 71) and Y - C(0, 72) are independent Cauchy variables, X + Y - C(0, T + Ta). (2) Use part (1) to determine the distribution of X, when X1,...,X, is a random sample from the Cauchy C(0, 1) distribution. What are the consequences of your finding, that is, does X estimate some meaningful quantity? Explain.

The Cauchy distribution with scaling parameter 7, C(0, 7), has density 1 TT1+ (z/7)2" 1 f(z; T) = ZER. and characteristic function (r) = eTal (you can take this for granted). (1) (optional). Show that if X ~ C(0, 71) and Y - C(0, 72) are independent Cauchy variables, X + Y - C(0, T + Ta). (2) Use part (1) to determine the distribution of X, when X1,...,X, is a random sample from the Cauchy C(0, 1) distribution. What are the consequences of your finding, that is, does X estimate some meaningful quantity? Explain.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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The Cauchy distribution with scaling parameter 7, C(0, 7), has density 1 TT1+ (2/7)" 1 f(z; T) = ZER. and characteristic function (r) = eTal (you can take this for granted). (1) (optional). Show that if X ~ C(0, 71) and Y - C(0, 72) are independent Cauchy variables, X + Y - C(0, T + Ta). (2) Use part (1) to determine the distribution of X, when X1,...,X, is a random sample from the Cauchy C(0, 1) distribution. What are the consequences of your finding, that is, does X estimate some meaningful quantity? Explain.
Transcribed Image Text:The Cauchy distribution with scaling parameter 7, C(0, 7), has density 1 TT1+ (2/7)" 1 f(z; T) = ZER. and characteristic function (r) = eTal (you can take this for granted). (1) (optional). Show that if X ~ C(0, 71) and Y - C(0, 72) are independent Cauchy variables, X + Y - C(0, T + Ta). (2) Use part (1) to determine the distribution of X, when X1,...,X, is a random sample from the Cauchy C(0, 1) distribution. What are the consequences of your finding, that is, does X estimate some meaningful quantity? Explain.
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