7.5.5. Let X be a random variable with the pdf of a regular case of the exponential class, given by f(x; 0) = exp[0K(x) + H(x) + q(0)], a < x
7.5.5. Let X be a random variable with the pdf of a regular case of the exponential class, given by f(x; 0) = exp[0K(x) + H(x) + q(0)], a < x
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Problem 1P
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![7.5.5. Let X be a random variable with the pdf of a regular case of the exponential
class, given by f(x; 0) = exp[0K(x) + H(x) + q(0)], a < x <b, y < 0 < 6. Show
that E[K(X)] = -q'(0)/p'(0), provided these derivatives exist, by differentiating
both members of the equality
[*exp|p(0)K(x) + H(2) + q(0)] dx = 1
with respect to 0. By a second differentiation, find the variance of K(X).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F32f77ee0-291c-46d0-b315-80fb2fd096d8%2Fca96e9c0-0d42-4055-8646-f7881076b7d7%2F4sg1pef_processed.jpeg&w=3840&q=75)
Transcribed Image Text:7.5.5. Let X be a random variable with the pdf of a regular case of the exponential
class, given by f(x; 0) = exp[0K(x) + H(x) + q(0)], a < x <b, y < 0 < 6. Show
that E[K(X)] = -q'(0)/p'(0), provided these derivatives exist, by differentiating
both members of the equality
[*exp|p(0)K(x) + H(2) + q(0)] dx = 1
with respect to 0. By a second differentiation, find the variance of K(X).
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