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
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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))](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F80beb3c7-0805-4123-826a-93aa0f72cc1c%2Fb546eb3a-7963-4219-adf5-045441006595%2Fzoqh4tk_processed.png&w=3840&q=75)
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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