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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-a/2 /2T fx (x) -00 < x < o. Define a discrete random variable Y by 1 P (Y = v3) = P (Y = -v3) P(Y = 0) = %3D Show that EXT = EY" for r = 1,2, 3, 4, 5.

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-a/2 /2T fx (x) -00 < x < o. Define a discrete random variable Y by 1 P (Y = v3) = P (Y = -v3) P(Y = 0) = %3D Show that EXT = EY" for r = 1,2, 3, 4, 5.

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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(c) fx(x) = (1/(20) Mx(t) = eut+oʻt°/2, -00 < I < 0; -0 <H <0, o > 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 fx (a) -00 < x < 0o. V27 Define a discrete random variable Y by P (Y = v3) = P (Y = -v3) P (Y = 0) = Show that EX EΥ" 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.
Transcribed Image Text:(c) fx(x) = (1/(20) Mx(t) = eut+oʻt°/2, -00 < I < 0; -0 <H <0, o > 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 fx (a) -00 < x < 0o. V27 Define a discrete random variable Y by P (Y = v3) = P (Y = -v3) P (Y = 0) = Show that EX EΥ" 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.
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