(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.
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter8: Sequences, Series, And Probability
Section8.7: Probability
Problem 39E: Assume that the probability that an airplane engine will fail during a torture test is 12and that...
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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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4061eb31-6ba2-4539-9b51-dd7b05481e7e%2Fe583ec77-903a-4079-ae0e-805548e897ba%2Fipogi3b_processed.png&w=3840&q=75)
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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