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1. (Review) (a) Suppose that X~ Cauchya and c> 0. Show that Y = CX ~ Cauchyca (Hint: This is a change of variable problem. First find the cdf for Y, then find the pdf by differentiating)

1. (Review) (a) Suppose that X~ Cauchya and c> 0. Show that Y = CX ~ Cauchyca (Hint: This is a change of variable problem. First find the cdf for Y, then find the pdf by differentiating)

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.6: Variation
Problem 37E
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= 1. (Review) (a) Suppose that X ~ Cauchya and c> 0. Show that Y cX Cauchyca (Hint: This is change of variable problem. First find the cdf for Y, then find the pdf by differentiating) (b) If X₁, ..., Xn are i.i.d. and X; ~ Cauchya, then Sn~ Cauchya (The point: Unlike in the various versions of the law of large numbers, Sn does not converge to a constant in any sense).
Transcribed Image Text:= 1. (Review) (a) Suppose that X ~ Cauchya and c> 0. Show that Y cX Cauchyca (Hint: This is change of variable problem. First find the cdf for Y, then find the pdf by differentiating) (b) If X₁, ..., Xn are i.i.d. and X; ~ Cauchya, then Sn~ Cauchya (The point: Unlike in the various versions of the law of large numbers, Sn does not converge to a constant in any sense).
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