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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 33E

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Properties of GPD
Let f be a GPD density function with paramters { and 3 such that
-(--+1)
f(x) = B-1 (1+
where B > 0, x > 0 when & > 0 and 0 <x < -B/E when { < 0.
prove :
•(+ + 5x)) =
E ( In (1+
and
E (In (1+ x)) = ç*k!, ke N.
E ( In (1+
where E denotes the expectation operator over the distribution. And EX < o if and
only if { < 1.

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