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Suppose f(x) is an even probability density so that f(x) = f(-x). Define g(x) = foo f(s) ds, S g(-x), ds, if x > 0, if x < 0. Why is g a probability density? If has chf (t), how can you express the characteristic function of g in terms of ?

Suppose f(x) is an even probability density so that f(x) = f(-x). Define g(x) = foo f(s) ds, S g(-x), ds, if x > 0, if x < 0. Why is g a probability density? If has chf (t), how can you express the characteristic function of g in terms of ?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Advanced Math Suppose f(x) is an even probability density so that f(x) = f(-x). Define g(x) = = [ff(s) ds, ifx>0, g(-x), if x < 0. Why is g a probability density? If has chf (t), how can you express the characteristic function of g in terms of ?
Transcribed Image Text:Advanced Math Suppose f(x) is an even probability density so that f(x) = f(-x). Define g(x) = = [ff(s) ds, ifx>0, g(-x), if x < 0. Why is g a probability density? If has chf (t), how can you express the characteristic function of g in terms of ?
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