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W/12 2.34 A distribution cannot be uniquely determined by a finite collection of mom example from Romano and Siegel (1986) shows. Let X have the normal c that is, X has pdf fx (x): 는2, -00

W/12 2.34 A distribution cannot be uniquely determined by a finite collection of mom example from Romano and Siegel (1986) shows. Let X have the normal c that is, X has pdf fx (x): 는2, -00

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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(a) P(X = x) = Mx(t) = e(e-1), = 0,1,...; d>0 (b) P(X = x) = p(1 - p)", Mx(t) = FDet, = 0, 1,... ; 0 <p<1 %3D %3D %3D 1-(1- Mx(t) = ellt+o?i? /2 -00 <2 < 00; -00 < u < o, o>0 (c) fx (x) = %3D 2.34 A distribution cannot be uniquely determined by a finite collection of moments, as this example from Romano and Siegel (1986) shows. Let X have the normal distribution, that is, X has pdf 1 e/2 V2T fx (a) = -00 < x < o. %3D Define a discrete random variable Y by P (Y = v3) = P (Y = -v3) 1 %3D P(Y = 0) = Show that EX = EY" for r = 1,2, 3, 4, 5. (Romano and Siegel point out that for any finite n there exists a discrete, and hence nonnormal, random variable whose first n moments are equal to those of X.) 2.35 Fill in the gaps in Example 2.3.10. (a) Show that if X1 fi(x), then EX = e*/2, r = 0, 1,.... So fi(x) has all of its moments, and all of the moments are finite. (b) Now show that
Transcribed Image Text:(a) P(X = x) = Mx(t) = e(e-1), = 0,1,...; d>0 (b) P(X = x) = p(1 - p)", Mx(t) = FDet, = 0, 1,... ; 0 <p<1 %3D %3D %3D 1-(1- Mx(t) = ellt+o?i? /2 -00 <2 < 00; -00 < u < o, o>0 (c) fx (x) = %3D 2.34 A distribution cannot be uniquely determined by a finite collection of moments, as this example from Romano and Siegel (1986) shows. Let X have the normal distribution, that is, X has pdf 1 e/2 V2T fx (a) = -00 < x < o. %3D Define a discrete random variable Y by P (Y = v3) = P (Y = -v3) 1 %3D P(Y = 0) = Show that EX = EY" for r = 1,2, 3, 4, 5. (Romano and Siegel point out that for any finite n there exists a discrete, and hence nonnormal, random variable whose first n moments are equal to those of X.) 2.35 Fill in the gaps in Example 2.3.10. (a) Show that if X1 fi(x), then EX = e*/2, r = 0, 1,.... So fi(x) has all of its moments, and all of the moments are finite. (b) Now show that
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