Explanation From the given information, Y = a X + b and X has a density function f X . Then, the cumulative distribution function of Y is F ( y ) = P ( Y ≤ y ) = P ( a X + b ≤ y ) = P ( X ≤ y − b a ) = F ( y − b a ) Differentiate with respect to y

Mathematical Statistics and Data Analysis

3rd Edition

ISBN: 9781111793715

Author: John A. Rice

Publisher: Cengage Learning

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Question

Chapter 2.5, Problem 62P

To determine

Prove that fY(y)=1|a|fX(y−ba) when X has a density function fX and Y=aX+b.

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Chapter 2 Solutions

Mathematical Statistics and Data Analysis

Ch. 2.5 - Prob. 1P Ch. 2.5 - Prob. 2P Ch. 2.5 - Prob. 3P Ch. 2.5 - Prob. 4P Ch. 2.5 - Prob. 5P Ch. 2.5 - Prob. 6P Ch. 2.5 - Prob. 7P Ch. 2.5 - Prob. 8P Ch. 2.5 - Prob. 9P Ch. 2.5 - Prob. 10P

Ch. 2.5 - Prob. 11P Ch. 2.5 - Prob. 12P Ch. 2.5 - Prob. 13P Ch. 2.5 - Prob. 14P Ch. 2.5 - Prob. 15P Ch. 2.5 - Prob. 17P Ch. 2.5 - Prob. 18P Ch. 2.5 - Prob. 19P Ch. 2.5 - Prob. 20P Ch. 2.5 - Prob. 21P Ch. 2.5 - Prob. 22P Ch. 2.5 - Prob. 23P Ch. 2.5 - Prob. 24P Ch. 2.5 - Prob. 25P Ch. 2.5 - Prob. 26P Ch. 2.5 - Prob. 27P Ch. 2.5 - Prob. 28P Ch. 2.5 - Prob. 29P Ch. 2.5 - Prob. 30P Ch. 2.5 - Prob. 31P Ch. 2.5 - Prob. 32P Ch. 2.5 - Prob. 33P Ch. 2.5 - Prob. 34P Ch. 2.5 - Prob. 35P Ch. 2.5 - Prob. 36P Ch. 2.5 - Prob. 37P Ch. 2.5 - Prob. 38P Ch. 2.5 - Prob. 39P Ch. 2.5 - Prob. 40P Ch. 2.5 - Prob. 41P Ch. 2.5 - Prob. 42P Ch. 2.5 - Prob. 43P Ch. 2.5 - Prob. 44P Ch. 2.5 - Prob. 45P Ch. 2.5 - Prob. 46P Ch. 2.5 - Prob. 47P Ch. 2.5 - Prob. 48P Ch. 2.5 - Prob. 49P Ch. 2.5 - Prob. 50P Ch. 2.5 - Prob. 51P Ch. 2.5 - Prob. 52P Ch. 2.5 - Prob. 53P Ch. 2.5 - Prob. 54P Ch. 2.5 - Prob. 55P Ch. 2.5 - Prob. 56P Ch. 2.5 - Prob. 57P Ch. 2.5 - Prob. 58P Ch. 2.5 - Prob. 59P Ch. 2.5 - Prob. 60P Ch. 2.5 - Prob. 61P Ch. 2.5 - Prob. 62P Ch. 2.5 - Prob. 63P Ch. 2.5 - Prob. 64P Ch. 2.5 - Prob. 65P Ch. 2.5 - Prob. 66P Ch. 2.5 - Prob. 67P Ch. 2.5 - Prob. 68P Ch. 2.5 - Prob. 69P Ch. 2.5 - Prob. 70P

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Prove that f Y ( y ) = 1 | a | f X ( y − b a ) when X has a density function f X and Y = a X + b .

Solution Summary: The author proves that f_Y(y)=

Prove that fY(y)=1|a|fX(y−ba) when X has a density function fX and Y=aX+b.

Chapter 2 Solutions