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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.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.1: Measures Of Center
Problem 9PPS
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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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