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.

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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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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