7. Let X₁, X2,..., Xn be independent variables, X; being N(µi, 1), and let y = = x² + x² +...+X²/2. Show that the characteristic function of Y is by(t) = 1 (1-2it)n/2 exp ite 1-2it where 0 = ²+²+ ...+. The random variables Y is said to have the non-central chi-squared distribution with n degrees of freedom and non-centrality parameter 0, written x² (n; 0).
7. Let X₁, X2,..., Xn be independent variables, X; being N(µi, 1), and let y = = x² + x² +...+X²/2. Show that the characteristic function of Y is by(t) = 1 (1-2it)n/2 exp ite 1-2it where 0 = ²+²+ ...+. The random variables Y is said to have the non-central chi-squared distribution with n degrees of freedom and non-centrality parameter 0, written x² (n; 0).
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![7. Let X₁, X2,..., Xn be independent variables, X; being N(µi, 1), and let y =
= x² + x² +...+ X² 2.
Show that the characteristic function of Y is
by(t) =
1
(1-2it)n/2
exp
ite
1-2it
where 0 = ²+²+ ...+. The random variables Y is said to have the non-central chi-squared
distribution with n degrees of freedom and non-centrality parameter 0, written x² (n; 0).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F761e1ae7-b81b-4bda-967b-d92bcf1c1ae3%2F61939b27-d9e4-4314-b716-20034a032043%2Fcpccz7e_processed.jpeg&w=3840&q=75)
Transcribed Image Text:7. Let X₁, X2,..., Xn be independent variables, X; being N(µi, 1), and let y =
= x² + x² +...+ X² 2.
Show that the characteristic function of Y is
by(t) =
1
(1-2it)n/2
exp
ite
1-2it
where 0 = ²+²+ ...+. The random variables Y is said to have the non-central chi-squared
distribution with n degrees of freedom and non-centrality parameter 0, written x² (n; 0).
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