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Let X - x? (r). Find (a) E (X³ – 2) where E (h (x)) = f° h (x) fx (x)dx. (b) the characteristic function of 1 +2X. (c) Suppose that X and Y are independent, and both follow a x² (r) distribution with moment generating func- tion (mgf), Mx (1) = My(t) = (1 – 21)~/2. Further, given that the mgf of the variance gamma distribution is Mz (1) = My.G.(.,a.p.p)t) = e#" (- ,find the (i) the mgf of Z = X – Y, and hence (ii) identify the distribution of Z.

Let X - x? (r). Find (a) E (X³ – 2) where E (h (x)) = f° h (x) fx (x)dx. (b) the characteristic function of 1 +2X. (c) Suppose that X and Y are independent, and both follow a x² (r) distribution with moment generating func- tion (mgf), Mx (1) = My(t) = (1 – 21)~/2. Further, given that the mgf of the variance gamma distribution is Mz (1) = My.G.(.,a.p.p)t) = e#" (- ,find the (i) the mgf of Z = X – Y, and hence (ii) identify the distribution of Z.

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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Let X - x² (r). Find (a) E (X³ – 2) where E (h (x)) = 6° h (x) fx (x)dx. (b) the characteristic function of 1 +2X. (c) Suppose that X and Y are independent, and both follow a x? (r) distribution with moment generating func- tion (mgf), Mx (1) = My(t) = (1 – 21)~r/2. Further, given that the mgf of the variance gamma distribution is Mz (1) = My.G.4),a.ß.p)(1) = e#! | ", find the (i) the mgf of Z = X – Y, and hence (ii) identify the distribution of Z.
Transcribed Image Text:Let X - x² (r). Find (a) E (X³ – 2) where E (h (x)) = 6° h (x) fx (x)dx. (b) the characteristic function of 1 +2X. (c) Suppose that X and Y are independent, and both follow a x? (r) distribution with moment generating func- tion (mgf), Mx (1) = My(t) = (1 – 21)~r/2. Further, given that the mgf of the variance gamma distribution is Mz (1) = My.G.4),a.ß.p)(1) = e#! | ", find the (i) the mgf of Z = X – Y, and hence (ii) identify the distribution of Z.
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