Let X ,X , ,X 1 2 n … be a random sample of size n from a population with mean μ and variance σ2 . (a) Show that X2 is a biased estimator for μ2 . (b) Find the amount of bias in this estimator. (c) What happens to the bias as the sample size n increases?
Let X ,X , ,X 1 2 n … be a random sample of size n from a population with mean μ and variance σ2 . (a) Show that X2 is a biased estimator for μ2 . (b) Find the amount of bias in this estimator. (c) What happens to the bias as the sample size n increases?
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.1: Measures Of Center
Problem 9PPS
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Question
Let X ,X , ,X 1 2 n … be a random sample of size n
from a population with mean μ and variance σ2
.
(a) Show that X2
is a biased estimator for μ2
.
(b) Find the amount of bias in this estimator.
(c) What happens to the bias as the sample size n increases?
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