Answered: k=1 The sample variance is an unbiased… | bartleby

Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 31E

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Let X₁, X2, X3, ..., Xn be a random sample with mean EX₁ = μ<∞, and
variance 0 < Var (X₂) = o² <oo. The sample variance of this random sample
is defined as
n
n
1
S²
1
(X-X) ²: (x²
Σx - nx
1-nt²
n-1
n-1
k=1
The sample variance is an unbiased estimator of o2. The sample standard
deviation is defined as
S = √S²,
and is commonly used as an estimator for o. Nevertheless, S is a biased
estimator of σ.

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