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6. Show that if f is a PDF and the integral [x²f(x) dx exists, then the integral |zx|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?)

6. Show that if f is a PDF and the integral [x²f(x) dx exists, then the integral |zx|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?)

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.CR: Chapter 13 Review
Problem 52CR
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6. Show that if f is a PDF and the integral [2²f(z) dz just do #6 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?) 280 #14 Let X be a continuous random variable with density function fx(x). Show that if x² fx (x) dx <∞, then +∞ |x|fx (x) dx <∞ . Hint: Except on the interval [-1,1], the first integrand is greater than the second integrand. -∞
Transcribed Image Text:6. Show that if f is a PDF and the integral [2²f(z) dz just do #6 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?) 280 #14 Let X be a continuous random variable with density function fx(x). Show that if x² fx (x) dx <∞, then +∞ |x|fx (x) dx <∞ . Hint: Except on the interval [-1,1], the first integrand is greater than the second integrand. -∞
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