a) Let X₁, X2X₁ denote a random sample from N(0, 2) distribution with probability density function: f(x;0²) = ze 20² 884x10 σ√₂π And let S² = be the estimator of o². 71 i) Show whether or not that S² is an unbiased estimator of a²? ii) Show that S² is a consistent estimator of a².
a) Let X₁, X2X₁ denote a random sample from N(0, 2) distribution with probability density function: f(x;0²) = ze 20² 884x10 σ√₂π And let S² = be the estimator of o². 71 i) Show whether or not that S² is an unbiased estimator of a²? ii) Show that S² is a consistent estimator of a².
Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015
1st Edition
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:HOUGHTON MIFFLIN HARCOURT
Chapter4: Writing Linear Equations
Section: Chapter Questions
Problem 12CR
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Question
![a) Let X₁, X₂,..., X₁ denote a random sample from N(0, ²) distribution with
probability density function:
1
f(x; σ²) = ze 20 -∞0 < x < 00
o√2π
And let S² =
be the estimator of a².
i) Show whether or not that S² is an unbiased estimator of o²?
ii) Show that S² is a consistent estimator of ².
71](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F59fc304e-f174-4073-beaa-c91da01ee65e%2Fe2a71f90-6d11-49c0-9d7a-53dc99364b31%2Fpzh891m_processed.jpeg&w=3840&q=75)
Transcribed Image Text:a) Let X₁, X₂,..., X₁ denote a random sample from N(0, ²) distribution with
probability density function:
1
f(x; σ²) = ze 20 -∞0 < x < 00
o√2π
And let S² =
be the estimator of a².
i) Show whether or not that S² is an unbiased estimator of o²?
ii) Show that S² is a consistent estimator of ².
71
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