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(a) From lectures we know (b) Let n Σ(-)² ~ x²(v). What is the value of ? i=1 = n 1 120 1 i=1 n- -Σ(X; - X) ². Determine Var(s), that is, the variance of the sample variance. (c) Assume now that we have observed data ₁,..., ER with sample variance s². Use the result from part (a) to find numbers an and bn, such that [ans, bns] is an exact 95%-confidence interval for ².

(a) From lectures we know (b) Let n Σ(-)² ~ x²(v). What is the value of ? i=1 = n 1 120 1 i=1 n- -Σ(X; - X) ². Determine Var(s), that is, the variance of the sample variance. (c) Assume now that we have observed data ₁,..., ER with sample variance s². Use the result from part (a) to find numbers an and bn, such that [ans, bns] is an exact 95%-confidence interval for ².

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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B4. Let X₁,... Xn ~ N(μ, o2) be independent random variables. 2 (a) From lectures we know (X=X) ²³. X₂ (b) Let n i=1 ~ x²(v). What is the value of v? n 1 *³ =, ²-₁, [(x₁ - x) ². Σ(x s n 1 i=1 Determine Var(s), that is, the variance of the sample variance. (c) Assume now that we have observed data ₁,...,n ER with sample variance s². Use the result from part (a) to find numbers an and b, such that [ans, bns] is an exact 95%-confidence interval for o².
Transcribed Image Text:B4. Let X₁,... Xn ~ N(μ, o2) be independent random variables. 2 (a) From lectures we know (X=X) ²³. X₂ (b) Let n i=1 ~ x²(v). What is the value of v? n 1 *³ =, ²-₁, [(x₁ - x) ². Σ(x s n 1 i=1 Determine Var(s), that is, the variance of the sample variance. (c) Assume now that we have observed data ₁,...,n ER with sample variance s². Use the result from part (a) to find numbers an and b, such that [ans, bns] is an exact 95%-confidence interval for o².
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