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If X is a random variable whose pdf belongs to the k-parameter exponential family, then k ac:@ d:(X) E - In a(@) i=1 k dc:(A) -d;(X) In a(0) -d;(X) Var - E i=1 foe > TASK # 28: Determine whether f (x) = 2²xe-Ax I(0,00) is a valid pdf or not. • If it is valid, can you use the theorem above to derive the variance of X~F? If Yes, find the mean and variance of X using the theorem above. • Iffis not valid, correct it to becomes a valid pdf then proceed to the part of finding its mean and its variance.

If X is a random variable whose pdf belongs to the k-parameter exponential family, then k ac:@ d:(X) E - In a(@) i=1 k dc:(A) -d;(X) In a(0) -d;(X) Var - E i=1 foe > TASK # 28: Determine whether f (x) = 2²xe-Ax I(0,00) is a valid pdf or not. • If it is valid, can you use the theorem above to derive the variance of X~F? If Yes, find the mean and variance of X using the theorem above. • Iffis not valid, correct it to becomes a valid pdf then proceed to the part of finding its mean and its variance.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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If X is a random variable whose pdf belongs to the k-parameter exponential family, then ac:@ d;(X) In a(0) E i=1 k aci@ d;(X) In a(@) Var ) - E -d;(X) > TASK # 28: Determine whether f (x) = 1²xe-1x I(0,00) is a valid pdf or not. If it is valid, can you use the theorem above to derive the variance of X~F? If Yes, find the mean and variance of X using the theorem above. If f is not valid, correct it to becomes a valid pdf then proceed to the part of finding its mean and its variance.
Transcribed Image Text:If X is a random variable whose pdf belongs to the k-parameter exponential family, then ac:@ d;(X) In a(0) E i=1 k aci@ d;(X) In a(@) Var ) - E -d;(X) > TASK # 28: Determine whether f (x) = 1²xe-1x I(0,00) is a valid pdf or not. If it is valid, can you use the theorem above to derive the variance of X~F? If Yes, find the mean and variance of X using the theorem above. If f is not valid, correct it to becomes a valid pdf then proceed to the part of finding its mean and its variance.
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