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6. Show that if f is a PDF and the integral [ 2² f exists, then the integral x² f(x) dx dx |x|f(z) dz exists. (This is from question number 14 on page 280 of the book which includes a helpful hint.) Why is this result important? (Why would we care about the existence of the second integral?)

6. Show that if f is a PDF and the integral [ 2² f exists, then the integral x² f(x) dx dx |x|f(z) dz exists. (This is from question number 14 on page 280 of the book which includes a helpful hint.) Why is this result important? (Why would we care about the existence of the second integral?)

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.3: Trigonometric Functions Of Real Numbers
Problem 65E
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6. Show that if f is a PDF and the integral [* x²ƒ(x) dx exists, then the integral |x|f(x) dx exists. (This is from question number 14 on page 280 of the book which includes a helpful hint.) Why is this result important? (Why would we care about the existence of the second integral?)
Transcribed Image Text:6. Show that if f is a PDF and the integral [* x²ƒ(x) dx exists, then the integral |x|f(x) dx exists. (This is from question number 14 on page 280 of the book which includes a helpful hint.) Why is this result important? (Why would we care about the existence of the second integral?)
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