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Show that the p.d.f. of Z? is given by g1(x) = cosh(vAr), x > 0, wh cosh(z) = }(e² + e-=) is known as the hyperbolic cosine function.

Show that the p.d.f. of Z? is given by g1(x) = cosh(vAr), x > 0, wh cosh(z) = }(e² + e-=) is known as the hyperbolic cosine function.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section: Chapter Questions
Problem 9T
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(a) Show that the p.d.f. of Z is given by g1(x) = e-(+)cosh(VAx), r > 0, where cosh(2) = (e +e) is known as the hyperbolic cosine function. (b) Use Taylor series of exponential functions to prove that 1 91(x) = %3D (2k)! k=0
Transcribed Image Text:(a) Show that the p.d.f. of Z is given by g1(x) = e-(+)cosh(VAx), r > 0, where cosh(2) = (e +e) is known as the hyperbolic cosine function. (b) Use Taylor series of exponential functions to prove that 1 91(x) = %3D (2k)! k=0
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