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Show that the Cauchy distribution with parameter = 0 and the t distribution with one degree of freedom are the same. Coci

Show that the Cauchy distribution with parameter = 0 and the t distribution with one degree of freedom are the same. Coci

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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Chapter 4 Rice 1. Recap: The Cauchy Distribution The probability density function of a Cauchy distribution (cd) with the location parameter, a and scale parameter b is given by f(x|a,b)=- -∞<x<∞, b>0. b z(b² +(x-a)²) ' Equation (1) is referred to as Cauchy (a,b). The standard form of (1) can be obtained by replacing a with 0 and b with 1 and is given by f(x|0,1)= 1 z(1+x²) -84x50 (2) Show that the Cauchy distribution with parameter 0 = 0 and the t distribution with one degree of freedom are the same. (na))
Transcribed Image Text:Chapter 4 Rice 1. Recap: The Cauchy Distribution The probability density function of a Cauchy distribution (cd) with the location parameter, a and scale parameter b is given by f(x|a,b)=- -∞<x<∞, b>0. b z(b² +(x-a)²) ' Equation (1) is referred to as Cauchy (a,b). The standard form of (1) can be obtained by replacing a with 0 and b with 1 and is given by f(x|0,1)= 1 z(1+x²) -84x50 (2) Show that the Cauchy distribution with parameter 0 = 0 and the t distribution with one degree of freedom are the same. (na))
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